Abstract - Ductile fracture in metallic materials occurs by the nucleation, growth, and linkage of microvoids within the bulk of the material. As a result, two dimensional techniques must be complimented with three dimensional techniques in order to completely characterize the fracture process. An extensive study of this process in copper alloys (pure Cu, Glidcop and brass) has been of great value in validating models for ductile fracture. In particular these studies reveal the importance of shear localization on a range of scales in void linkage. More recently we have focused on Mg which exhibits much poorer formability than fcc materials at room temperature. These experiments use a combination of tensile testing coupled with scanning electron microscope (SEM) imaging, electron backscattered diffraction (EBSD) patterning, and micro computed x-ray tomography (XCT) to analyze void linkage. The void linkage process is very different than in the fcc materials. In magnesium, void fraction and void orientation have a weak influence on the failure strain due to the premature linkage of voids. EBSD analysis has shown that this premature void linkage is associated with the failure of twin and grain boundaries. The results suggest that (in contrast with more ductile fcc metals) the local microstructure has a significant impact on void linkage.

This study aims at understanding the effects of load path changes on the fracture locus of ductile materials. Guided by previous theoretical analyses, we design an experimental program to probe the path-dependence of the fracture locus of mild steel under axisymmetric loading conditions. Under such circumstances, failure occurs by microvoid growth to coalescence, as confirmed by post-mortem fractography. Following the literature, the fracture locus is given in terms of a strain to failure versus a strain-weighted average of stress triaxiality. The strain to failure was recorded for each loading path and the locus relating it to average triaxiality was constructed. This process was repeated for a set of non-proportional loading paths. By way of comparison, a fracture locus that best represents proportional loadings was also determined using notched bar experiments. Finite element calculations were used to determine the evolution of stress triaxiality at failure locations. The findings indicate that there is generally no one-to-one relationship between the average loading triaxiality and the strain to failure. In addition, variations of the latter due to nonproportional loadings can be so large that care should be taken in using fracture criteria based on a hydrostatic-stress dependent critical strain.

Magnesium alloys are prime candidates for weight reduction in automotive and aerospace industry. These alloys, however, suffer from poor formability and catastrophic fracture after limited necking at room temperature. The deformation behavior of magnesium alloys has been studied extensively over the past decade but their damage and fracture behavior is poorly understood. In this study, the anisotropic deformation and fracture behavior of two rolled Mg alloys (AZ31-H24 and WE43) are investigated using tension, compression and tensile notched bar experiments. In AZ31, A weak sensitivity of the strain-to-failure to stress triaxiality is found, at variance with other material systems. The macroscopic features of fracture indicate a high propensity for shear localization in simple tension, including for round bars. High triaxiality introduced by the means of notches changes the macroscopic features and result in a flat fibrous fracture surface with almost equal area reduction compared with smooth bars. Damage mechanisms are studied using post-mortem fractography and specimen sectioning after interrupted testing. Most surfaces exhibit (i) dimples indicating ductile nature of fracture by void nucleation and growth (ii) small smooth facets related to deformation twins (iii) second phase particles at the fracture surface implying their contribution in fracture (iv) splits on the fracture surface in the direction perpendicular to both loading and short-transverse directions. There are very large facets observed on notch bars in different location of fracture surface which are probably related to coalescence of cracks developed along twin boundaries. These features are not observed in smooth bars. Transverse sectioning of materials at the incipient cracking state reveals that incipient cracks are formed near surface and initiated at either (a) deformation twins (contraction or double twins) and their junction with each other or (b) second phase particles and their interface with the parent matrix. Plastic anisotropy, shear localization and coalescence controlled crack formation are proposed as the mechanisms controlling fracture properties. By way of contrast, the ductility of WE43 is found to be quite sensitive to stress triaxiality. Preliminary investigations suggest an intergranular fracture mode associated with grain-boundary precipitates.

Damage evolution in most ductile metals is characterized by the nucleation, growth and coalescence of small internal voids. In Al alloys, the primary void population generally nucleate by the fracture of iron rich intermetallic particles, while a second population of voids can nucleate on smaller particles such as the Cr or Mn rich dispersoïds. The objective of this study is to understand what are the key factors controlling the damage behaviour of various alloys of the 6xxx series, in order to build up a quantitative model for the prediction of the fracture strain. More specifically, the 6005A, 6061 and 6056 alloys are considered. A wide variety of hardening responses are produced by performing annealing at different temperatures and for different times. The key result motivating this investigation is that samples with similar yield strength show very different fracture strain for these three alloys, even though the inclusion volume fraction is comparable.
Two types of models are developed to rationalize the different results. Both are based on micromechanics. The first one relies on an enhanced Gurson type framework. The second one is a cellular automaton which involves a more elementary description of the void growth process but which takes into account the statistics of the inclusion distribution and failure strength. The models are identified and validated based on tensile tests of various alloy tempers, on in-situ tension 3D X-ray synchrotron tomography and on a detailed microstructure analysis. The effect of the main parameters influencing the fracture strain are investigated, namely the initial porosity, the nucleation stress, the intermetallics spatial distribution, the strain hardening capacity and the presence of a second void population. The importance of properly taking into account statistical aspects is crucial to generate quantitative predictions.

Critical fracture strain criteria may be useful for large-scale simulations of ductile fracture under general loading conditions. In whichever way it is defined, the strain to failure of a ductile material depends on the stress state (stress triaxiality, Lode angle, etc.) This relationship defines a fracture locus, which for isotropic materials can be represented by a surface. However, the only fracture locus that is intrinsic to a given material is the one obtained under proportional loadings (fixed triaxiality and Lode angle). In other words, the only well defined fracture locus is not experimentally accessible for it is difficult in experiments to ensure a proportional loading path all the way to failure over the desired range of stress states. An important question, therefore, is that of what types of nonproportionality lead to the stronger deviations from the proportional fracture locus. This talk addresses this question and related issues. First, numerical experiments using micromechanical finite element calculations are used to discover trends, state a conjecture and help design physical experiments. Next, real experiments on mild steel are conducted to confirm or falsify the conjecture. Finally, analysis is conducted using a simple damage model incorporating an internal state variable, which captures the essence of findings from numerical and real experiments. The model predictive capabilities are used to explore the parameter space in ways that are not easily accessible to experimentation. The maximum deviations from the proportional fracture locus are quantified for various loading types.

The ductile failure process driven by void nucleation, growth and coalescence, is well understood under conditions of high stress triaxiality, but less so for stress states at low triaxiality. However, recent micromechanical studies show that under shear dominated stress states, void driven ductile failure may even occur when triaxiality becomes negative, but with a very different behaviour. Under such circumstances, voids deforms into penny shaped cracks that rotate and start to interact in a manner that leads to coalescence and material failure. This behaviour has also been observed experimentally, and continuum damage models have emerged that address this phenomenon. Moreover, it has been observed that the critical effective plastic strain is not monotonically related to triaxiality in some metallic alloys. In such alloys, the distinction between axisymmetric stress states and shearing stress states becomes important when ductility is to be assessed. The distinction between axisymmetric and shearing stress states can be expressed by means of the third deviatoric stress invariant J3 or by the Lode parameter. By contrast, in experiments carried out on metallic alloys where the plastic flow properties depend markedly on J3, the distinction between axisymmetric and shearing stress states seems to be less important for ductility. This will be illustrated by results from an analysis based on a Gurson type of model where the plastic flow properties of the matrix material also depend on J3.

Ductile crack propagation in metallic sheets or plates often starts in mode I as a flat triangle. After some limited extension, the crack becomes slanted and propagates under local mixed mode I/III.
This phenomenon was observed both in steel and aluminum alloys provided work hardening is limited.
In this study, the ``computational cell'' methodology proposed by Xia and Shih (1995) is used to analyze the flat/slant propagation transition. A crack path is predefined within a 3D mesh. Material behavior for the elements within the path obeys a GTN-type material behavior whereas the other elements remain damage free. The macroscopic dissipation rate is studied as a function of the assumed crack tilt angle.
It is shown that a minimum is always reached for an angle equal to 45°. This correlates well with the variation of the crack tip opening angle (CTOA) or the mean plastic deformation along the crack path. Stress and strain states in the stable tearing region hardly depend on the assumed tilt angle. A parametric study shows that flat to slant fracture transition is less likely to occur in materials having high work hardening and favored if additional damage is caused by the local stress/strain state
(plane strain, low Lode parameter) in the stable tearing region.

Single crystal Ni-based superalloys were introduced in the early 1980s and since then have been widely used in turbine aerofoils in jet engines. The desire for weight reduction and the use of advanced metal cooling schemes tends to drive designs toward thinner airfoil walls. Creep tests on Ni-based superalloy specimens have shown greater creep strain rates and/or reduced creep rupture times for thinner specimens than is predicted by current theories. This is called the thickness debit effect. To investigate the mechanism of the thickness debit effect, isothermal, constant nominal stress creep tests were carried out on uncoated PWA1484 Ni-based single crystal superalloy sheet specimens under two test conditions: 760 deg. C/758MPa and 982 deg. C/248MPa. Based on the experimental observations and finite element analyses of porosity evolution, we developed a simple nonlinear parallel spring model with the spring constitutive relation representing both material creep and evolving damage. The bulk damage mechanisms accounted for are the nucleation of cleavage-like cracks from pre-existing voids and, at the higher temperature, void nucleation. The surface damage mechanisms modeled at the higher temperature are an oxidation layer, a γ&’-precipitate free layer and a γ&’-precipitate reduced layer. Results for the creep response and for the thickness debit effect are in qualitative and, in some cases, quantitative agreement with the experimental results. The simplicity of the model also allows parameter studies to be undertaken to explore the relative roles of bulk and surface damage as well as the relative roles of cleavage-like cracking and void nucleation in the bulk.

Ductile fracture has been studied extensively over the last five decades. It is composed of three steps: nucleation of cavities, growth of these nucleated cavities and coalescence leading to the final fracture. The complexity of this process has been historically studied by standard microscopy and this has permitted to validate damage models for the three different steps.
Damage in ductile materials can nowadays be imaged in 3D using different methods at different scales. The most commonly used of these recently appeared methods in the field of ductile damage is probably X-Ray Computed Tomography (XRCT) because of its multimaterial, multiscale and non destructive character.
3D imaging (if non destructive like it is the case for XRCT) can also be coupled with in situ loading of the sample (in situ tension in the present paper). The observation of the evolution of the microstructure under load in 3D allows to understand and image separately the three steps of ductile damage as for example in the case of tension of high strength steels.
This presentation will illustrate this combination of techniques and how we have used it in recent studies in order to understand the deformation of heterogeneous materials. Very high resolution and high acquisition rates, two new tendancies in this field, will also be illustrated.

X-ray microscopy enables three-dimensional investigation of heterogeneous materials at sub-100 nm resolution using computed tomography. The method is placed in-between X-ray microfocus tomography which provides less resolution and transmission electron microscopy which is limited in sample size especially along the optical axis. Cracks in materials can be enhanced by Zernike phase contrast, and long working distances allow an easy integration of attachments for in-situ studies. We present a miniaturized dual cantilever beam tester that is fully integrated into a laboratory X-ray microscope. A closed-loop piezo actuator is used for precise control of the crack propagation. Tomographies are acquired at several load steps to visualize the progress of the crack path which makes this methodical approach complementary to well-known macroscopic tests in fracture mechanics. Typical dimensions of the specimen are 50×50×500 µm³. Recent high-performance microprocessors take advantage of materials with low dielectric constants that are used to isolate on-chip interconnects. However, the Young's modulus and fracture toughness are usually reduced for these materials. We demonstrate local crack propagation studies at on-chip interconnect stacks of microelectronic devices. The results provide a better understanding of failure mechanisms and provide input for design.

The relatively new cross-correlation-based analysis of EBSD patterns has been used to map variations of elastic strain and the lattice rotation tensors within selected grains of cyclically deformed metals. The method gives a sensitivity of ~10^-4 rads in lattice rotation, ~10^-4 in elastic strain (which is equivalent to ~15 MPa stress in Ti) [1, 2]. Maps of measured rotation gradients have been used within the Nye geometrically necessary dislocation (GND) framework to generate maps of the GND density distribution [3], while the elastic strains allow calculation of the stress tensor.
Examples will be given for Ti-6Al-4V polycrystals deformed in monotonic tension, fatigue and dwell fatigue. Comparison will be made for these three cases of the internal stress and dislocation density probability distributions over the sampled areas. The effects of grain size and grain orientations on these distributions will also be presented. Modified scatter plots will be used to show the extent of correlation between dislocation density and internal stress. Correlation of stress and dislocation density with location within the microstructure will also be shown using metrics such as distance to the nearest grain boundary or triple junction or β-phase region. Comparison with available finite element or spectral analysis crystal plasticity simulations will be made.
[1] Wilkinson, A.J., G. Meaden, and D.J. Dingley, High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity. Ultramicroscopy, 2006. 106(4-5): p. 307-313.
[2] Britton, T.B. and A.J. Wilkinson, High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations. Ultramicroscopy, 2012. 114: p. 82-95.
[3] Nye, J.F., Some geometrical relations in dislocated crystals. Acta Metallurgica, 1953. 1(2): p. 153-162.

X-ray microscopy (XRM) executed both in the laboratory and synchrotron have demonstrated critical analysis and characterization of materials on the meso-, micro-, and nanoscales. [1] Understanding the three-dimensional (3D) material structures of volumetric features such as struts, as well as distribution of defects such as inclusions, cracks or voids are fundamental to understanding how materials form, deform and perform. In structural metals, ductile damage is thought to occur through an evolving process of void nucleation, growth and coalescence that leads to the ultimate failure of a material (e.g. spall layer formation in high tensile copper). However, the dynamic damage models available to the theoretical and experimental communities require statically robust datasets that track microstructural changes and damage evolution due to mechanical loading. Recent state of the art advances in metallographic characterization have transformed from 2D to 3D techniques, yielding more robust and statistically relevant datasets for damage models. In many instances, these 3D datasets have revealed features previously missed in 2D, however, 3D tomographic techniques have not yet been fully verified as traditional 2D damage quantitative techniques. Validation efforts for 3D techniques to provide quantitative characterization beyond qualitative descriptions will be presented for high-purity copper. [2] Results will also be presented to describe fundamental mechanisms of void nucleation, growth, and coalescence in incipient spall experiments on high-purity copper samples with a known grain sizes to examine the relationship between these defect characteristics and void growth. [3] Characterization results of the resultant damage was performed via standard optical and electron backscatter diffraction (2D) analyses, alongside X-ray microscopy (3D) which provided an in situ non-destructive method of microstructure characterization complementary to traditional 2D microscopy.
References:
1. Merkle, A. P. & Gelb, J. Microscopy Today 21, 10-15 (2013).
2. Patterson, B. M., et al. Microscopy and Microanalysis 18, 390-398 (2012).
3. Escobedo, J. P. et al. Journal of Applied Physics 110, 033513-033513-13 (2011).

Uniform and multilayered nanocomposites are of growing interest due to their desirable mechanical properties and their performance under high stress, wear, and impact conditions. Composite structures offer an opportunity to combine the useful properties from multiple materials. Controlled variations in composition and microstructure within a composite material allow for tunable local variations in properties. The simplest version of such a variation is to periodically change the composite volume fraction to create a multilayered composite material. Such structures would have hard layers to maintain strength and soft regions to allow for plasticity and prevent brittle failure. We are able to manufacture uniform and layered composites of nickel matrices embedded with alumina nanoparticles using electrodeposition. In this method a rotating disk electrode (RDE) is used to directly control the rate of particle incorporation. Uniform composites are made by holding a constant RDE rotation rate while layered composites are manufactured by oscillating the rotation rate during deposition. We have demonstrated this novel manufacturing process for large-scale samples, several square centimeters in area and hundreds of µm thick, while maintaining sub-micron microstructural resolution. Here we present the micro-tensile and hardness behavior of these nanocomposites. The uniform composites show a substantial increase in yield strength compared to that of the pure nickel, but this strengthening also resulted in significant loss of ductility and toughness. The multilayered samples showed unique behavior by maintaining hardnesses and yield strengths comparable to the uniform composites while also substantially increasing the ductility of the material.

The silica glass is a fundamental of various kinds of glasses and is widely used, e.g., in the optical fibers. Due to the brittleness of the silica glass, the micro-cracks and impurities contained in it influence sensitively its strength and lifetime. It is experimentally well known that the water molecules, which migrate into the silica glass from the moisture environment, react with the silica atoms to beak the stretched Si-O bond, resulting in accelerated breakage of the glass. The reaction mechanism of the bond breakage has been believed to follow the Michalske-Freiman reaction model (H2O + -Si-O-Si- => -Si-OH + HO-Si-).
In this paper, we propose a novel reaction model between the water molecules and silica glass by performing reaction-dynamics simulation using the hybrid quantum-classical method. In the hybrid method, the quantum region treated with the electronic density-functional theory (DFT) is embedded in a large classical system: the quantum and classical regions couple mechanically with each other. We perform the hybrid simulation of a silica glass system (about four thousand atoms) with water molecules inserted in it. We set the quantum region as that composed of the water molecules and their surrounding atoms. For fast computation we use the real-space grid based implemented of the Kohn-Sham DFT (RGDFT) code. In the cases where a single water molecule exists in the system, we do not observe any reaction between the water and the silica atoms even in highly stretched or expanded systems contrary to the Michalske-Freiman reaction model mentioned above. In the cases where two molecules are placed initially at neighboring sites, they attract each other to form a water-dimer in a relatively large site of the silica glass. Those self-dimerized water molecules react quite sensitively with the silica atoms to break the Si-O bond. Detailed analyses about the reaction mechanisms are presented.

Brittle materials experience strength enhancement as their size reduces -- this is related to the probability of smaller defects in smaller size structures. In this study, we investigate the strength size effect in polycrystalline silicon (polysilicon) micro tensile bars. An in situ tensile test using different sample sizes of polysilicon has been developed. The test system utilizes a chevron thermal actuator to apply load to the samples. A voltage applied across the thermal actuator legs causes them to expand by joule heating. This expansion induces a force on the micro tensile bars and the tensile bar fractures upon applying sufficient load. The displacement is recorded throughout the experiment and the fracture strength is calculated from linear finite element analysis. Five different samples were tested, two of which were uniform tensile bars with 70 and 7 mu;m gauge length. The other three were double edge notched (DEN) tensile bars with notch length of 4 mu;m and notch radii of 4, 1 and 0.5 mu;m respectively (4/4, 4/1 and 4/0.5). Linear finite element analysis is used to determine the strength of notched tensile bars, where the strength is the value of the maximum stress in the notch (stress at notch root).
The strength of brittle materials is not a single value even for the same size structures. Therefore, a probabilistic approach is used to analyze the strength distribution. Weibull weakest link theory is first used to analyze the data and predict the size effect. The experiments clearly show a size effect behavior, where the characteristic strength (strength at probability of 0.63) has changed from 2.7 GPa for the larger size specimen (70 mu;m tensile bar) to 4.25 GPa for the smaller size specimen (4/0.5 DEN tensile bar). The data of the larger sample was fitted with a Weibull three parameters function and the fitted parameters were used to predict size effect for smaller size tensile bars. A strength prediction by the Weibull function performed very well for the 7 mu;m tensile bars and relatively well for 4/4 notched tensile bars; however, it failed to predict strength distribution of smaller size notched tensile bars (4/1 and 4/0.5)
A new numerical approach has been developed for the treatment of strength distribution of brittle materials. The approach relies on generating random volumes and assigns a flaw size to each volume. The flaw size distribution is assumed to be described by a power law function where the constants are determined by fitting one set of strength data. Then, the fitting constants can be used to estimate size effects for other different size tensile bars. This approach is compared to Weibull weakest link theory. Both methods are good at estimating size effects of large size tensile bars. However, the new approach predicts an upper bound to the strength while the Weibull does not. Furthermore, the new approach predicted the size effect of smaller size tensile bars better than the Weibull distribution.

A systematic investigation of stability and growth of long shear-mode cracks started only after 1980. In the pioneering stage, fatigue cracks loaded particularly in remote mixed modes I+II, I+III were studied along with complicated fracture morphologies (factory roofs) obtained in torsion. A significance of the extrinsic (shielding) component of crack-growth resistance caused by interaction of asperities in the crack wake (friction-based closure) was already recognized. A negative role of superimposed mode I loading (accelerated crack growth) was described, e.g., in [1]. On the other hand, a positive effect of a superimposed static mode III on the cyclic mode I loading was reported and quantitatively described by Pineau et al., e.g. [2]. During the last 20 years some sophisticated models of extrinsic component of the resistance to shear-mode crack growth were developed by considering principal micromechanisms of shear-mode closure. On the other hand, our understanding of the intrinsic (effective) component is still on a very low level. There are several related topics deserving a close attention to be paid to: (i) experimental determination of intrinsic crack-growth thresholds in modes II and III; (ii) comparison of mode II and mode III crack growth rates and (iii) competition between shear and opening modes (mode I branching).
This presentation reports on recent experimental results achieved in the above mentioned areas using samples made of polycrystalline iron, titanium and austenitic steel. In accordance with theoretical prediction [3], intrinsic thresholds (crack growth rates) were found to be less (higher) than those in mode III for all investigated materials. Stereophotogrammetry of fracture surfaces revealed maximum mode I branching angles in the austenitic steel and the lowest ones in the polycrystalline iron where the cracks propagated predominantly along the maximum shear plane. Underlying principles of these phenomena are discussed in terms of discrete-dislocation models and materials microstructure.
References
[1] Tschegg E. K.: Mater. Sci. Eng. 54 (1982), 127-136.
[2] Hourlier F., Pineau A.: Fatigue Engng. Mater. Struct. 5 (1982), 287-302.
[3] Pokluda J., Pippan R.: Fatigue Fract. Engng. Mater. Struct. 28 (2005), 179-185.

Non-smooth alternating stress fields are frequently observed at stress concentrations: corners, notches or holes in components; because of the introduction of residual stresses or because a combination of both: stress concentrations and residual stresses. The ways to produce an accurate analytical approach are reviewed.
As a practical exercise, an estimation of fatigue crack growth is shown for a crack along the side of a beam in bending. It is the case for a three- and four-point bending test specimens. There is no solution available in the literature (other than finite element calculations) to compute the Stress Intensity Factors (SIFs) for this configuration, because it results in a three-dimensional problem.
The solution is approached considering the beam sliced initially in a horizontally direction and afterward considering also vertical slices. For those slices there are analytical expressions to compute SIFs (which are varying along the crack front locations) and correction factors that account for the effects of free boundaries. The limitations of this technique are shown; also the approximations and decisions, which seem more reasonable to make, are discussed.
Once the SIFs are estimated, it is possible to approximate the propagation rate along the crack front. Hereafter an assessment about the remaining fatigue life, until reaching the material critical SIF, is obtained. Other techniques are possible: finite element computations with cohesive elements, carrying out the appropriate fatigue experiments (4-point bending). This allows to ascertain the degree of approximation reached by the other analytical approaches.
Experiments have been conducted on an ultrafine grain steel four-point bending test-piece. A crack is grown from the bottom side to about one third of the beam height and then it is repositioned to locate the crack at the beam edge side. After a given number of cycles the specimen is heat tinted to track the fatigue crack growth. Eventually the predictions and the experimental results are compared and discussed.

Al-Mg 5xxx alloys are desirable in a wide array of structural applications that require a weldable alloy with good corrosion resistance. However, significant changes in the fatigue crack growth behavior have been shown to occur after low temperature exposures for long times (e.g. 1000's hrs). Commercially available 5xxx alloy plates have been thermally exposed to temperatures of 60°C, 70°C, 80°C, for up to 15,000 hrs. Significant changes to the hardness, tension and fatigue crack growth behavior have been observed after such exposures. In particular, longitudinal splitting in the short-transverse (ST) direction has been exhibited during fatigue after sufficient time and temperature exposure combinations. The evolution of properties (i.e. mechanical/fracture/fatigue) and microstructures (e.g. grain boundary segregation, grain boundary precipitation, etc.) with thermal exposure under these conditions will be presented, followed by attempts to remediates the property degradation.

Cold spray is a novel and promising technology to obtain surface coating. Notwithstanding the several technological advantages with respect to other processes, its diffusion is somewhat limited by the limited knowledge about the mechanical properties of the cold sprayed materials and in particular, their fatigue behavior. Reference data concerning fatigue behavior of coated specimens are controversial and different material system show different behavior. The aim of this study is to distinguish the parameters involved and their effect on fatigue behavior of cold sprayed systems. The material investigated is the Al alloy 6082 and the coating is obtained by means of similar material deposition. This has technological interest in view of practical application of cold spray in repair and maintenance. In addition, a simpler system with similar material properties is studied to decrease the number of parameters involved and to be able to study their effect more precisely and complete the range of previous investigations. Micro-structural observation, micro-hardness measurements, surface roughness and X-Ray diffraction (XRD) measurement of residual stress were performed on the sprayed material. Tubular coating tensile test was also carried out to characterize the cohesion of the coating. The majority of fatigue tests data of cold sprayed material, available in the literature, was reported for the system of substrates-coating with the same range of thickness subjected to bending. This means that the interface of the coating with the target material is subjected to a fatigue stress much less than the one on the free surface, increasing the risk of overestimation of the fatigue limit. To overcome this deficiency rotating bending fatigue tests were executed on specimens with a diameter equal to 6mm in this study. This reduces the stress gradient and as another benefit makes the tests results comparable with most of the fatigue data available in literature. The results showed that the cold spray process developed significant compressive residual stress in both deposited material and the substrate. Cold spray coating is able to increase the fatigue limit by 14.7 %. The results of the tests and the post-mortem observations allowed to quantify the effect of cold spray and to clarify the failure mechanisms. Based on the result of present investigation and data available in literature, critical discussion on four important parameters including interface quality, material properties, deposition parameters and residual stress and their effect on fatigue behavior of coated specimen is conducted.

Concepts are introduced to address microstructure-sensitive modeling of fatigue of advanced structural alloys, with a focus on variability of fatigue response with microstructure. In particular, we consider sensitivity of fatigue crack formation and early growth at the scale of the grains in polycrystalline and polyphase microstructures to facilitate preliminary parametric design exploration aimed at comparing a range of microstructure morphologies for nominally the same composition. Scatter in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) is computationally assessed using multiple statistical volume elements and the distribution of computable mesoscopic Fatigue Indicator Parameters (FIPs). The distribution of indicated crack formation sites and relative growth in HCF are considered as a function of strain amplitude in alpha-beta Ti alloys and Ni-base superalloys. To compare microstructures based on the criterion of a given low probability fatigue life (e.g., 1% probability) for remote applied loading conditions, extreme value statistical distributions are used to characterize the maximum FIPs corresponding to a large number of computational statistical volume elements for Ni-base superalloys and Ti-64 alloys. The concept of marked correlation functions is introduced as a means to quantify the role of multiple microstructure attributes that couple to enhance the extreme value FIPs, providing a tangible means of feedback to modify microstructure to facilitate design of alloys with improved fatigue properties. Prospects for future advances are briefly discussed, including multiaxial stress state and load sequence effects.

Grain boundaries (GB) often play an essential role in the deformation and damage processes of metals and alloys submitted to creep or fatigue. Depending on the material and testing conditions, crack initiation from GB could be directly related to their intrinsic “brittle” behaviour or to complex oxidation/corrosion - deformation interactions. However, for a great number of alloys, the origin for cracking at GB comes from stress-strain incompatibilities between neighboring grains especially due to the crystallographic anisotropy of elastic and plastic properties. Moreover, the interaction of slip bands with the boundaries is another source of damage, the possible transfer of dislocations through the GB remaining a key question. In this field, the local 3D configuration, the nature of the GB, and the crystallographic orientation of the neighbours are essential parameters to be considered.
In this study we propose to focus on the development of slip bands and on the early stages of cracking at GB in a Udimet 720Li superalloy with a coarse grains structure. Mechanical experiences have been performed at 20°C: monotonic tensile tests especially developed in situ in a scanning electron microscope to focus on the slip bands activity and fatigue tests rapidly stopped to focus on the early stages of damage. The objective was to identify the microstructural parameters that could distinguish local configurations in favor of crack initiation to the others. The analyses concerned the influence of the crystallographic orientation of neighboring grains since it governs the more or less easy development of plasticity in each grain. For that, all the samples were entirely characterized by electron backscattering diffraction (ebsd) before or/and after testing. Statistical distributions concerning the slip bands (Schmid factor, number and length of slip bands) have been established.
A special attention has been paid on the deformation features in zones where slip bands interact with the GB. Different configurations were studied considering the possibilities of slip transfer through the GB and the interactions between slip systems developed in the neighboring grains. For a low fraction of GB, the development of intense elastic lattice rotations confined in very small volumes that appear near a GB ahead of a slip band active in the neighbor grain has been evidenced. This phenomenon has been observed for configurations where the plastic activity is easy in one grain and clearly more difficult in its neighbour. The crystallographic rotation that could reach up to 10° in the central part of these “microvolumes” has been more precisely characterized by an ebsd cross correlation method (Cross Court software) and the associated 3D local elastic strain-stress state has been estimated. Analyses performed on fatigued specimens have shown that, under the investigated testing conditions, such phenomenon plays a major role in the crack initiation process.

Metal fatigue is an important mechanism for failure of structural components. The presented work will demonstrate a method to predict the stable crack growth behavior of ductile metals, and relate it to fatigue. The method combines fracture mechanics and atomic scale physics to predict quantitative stable crack growth rates at small strains. The strain distribution near a crack tip is approximated using a solution from linear elastic fracture mechanics. The strain distribution is combined with the theoretical strength to predict crack growth rate curves. To validate this approach the predictions generated for a variety of simple metals are compared to experimental data from literature.

Fatigue crack growth by the striation mechanism is thought to occur with dislocation emission along a pair of strain bands oriented 45° from the direction of crack growth. To study the dislocation structures formed by fatigue crack growth we have utilized strain computation by Electron Backscatter Diffraction (EBSD) as well as direct visualization in the Transmission Electron Microscope (TEM) of an arrested fatigue crack, while comparing our results with in situ Digital Image Correlation. The material selected was Haynes 230, a planar slip material. The EBSD data revealed that the strain was in bands, the deformation within the bands was inhomogeneous, and strain was concentrated at grain boundaries. TEM samples were extracted from the surface over distances extending from the crack tip to 800 mu;m using focused ion beam machining. The evolved microstructure beneath the surface increased in complexity as the crack tip was approached. The dislocation structure primarily consists of planar slip bands that demonstrate an increase in dislocation density and a decrease in inter-band spacing as the crack tip is approached. The microstructure in the immediate vicinity of the crack tip changes from the planar slip structure, showing evidence of higher strains. Immediately at the crack tip, the microstructure has refined into a nanograin equiaxed structure that becomes progressively larger further away from the crack. At a distance of 200 nm from the crack flank, the microstructure transitions to a banded subgrain structure that extends for several micrometers. The near crack structure is more complex than predicted to develop under fatigue loading of a planar slip material. To ascertain if this near crack microstructure is general or unique to the surface, it will be compared with the microstructure beneath striations. The generality of this microstructure refinement across face-centered cubic structured materials will be determined by comparison with that generated in Cu.

The stainless steel alloy 718 is highly sensitive to oxidation assisted intergranular cracking (OAIC) in a wide range of temperature and mechanical loading types. However, as a great number of metallurgical states can be designed to fullfill the requirements of various areas of application, this alloy is often used. It is thus essential to increase its resistance to OAIC. The present paper will cover, when it exists, the coupling between oxidation processes and mechanical behaviour at different scales. In particular, dynamic strain aging and flow instabilities (Portevin-LeChatelier) strongly affect OAIC. Among the possible mechanisms explaining this damaging process, the effect of atomic transport and segregation at the grain boundaries during the DSA regime leading to an increase of intergranular oxidation kinetics is investigated. Results show that refractory solute atoms as well as interstitials can be dragged by dislocations. Assuming that this phenomenon is involved in the damaging process, critical mechanical tests were carried out to assess the validity of the proposed mechanism. Moreover different heat treatments were applied to the same heat leading to reduce or inhibit OAIC.

Irradiation embrittlement of structural steels is a critical issue for light water reactor life extension, advanced fission reactors and future fusion energy systems. This presentation addresses two important embrittlement issues. First, irradiation hardening-induced shifts in the toughness-temperature relation are described in the framework of the Master Curve (MC) method. Note that in both RPV and 9Cr tempered martensitic steels, increases in yield strength can reach levels in excess of 500-600 MPa. Measurements of the dynamics of crack initiation and arrest toughness in cleavage oriented semi-brittle iron single crystals are reviewed. These results confirm that the dynamics of cleavage and dislocation mediated plastic flow are essentially identical. The single crystal data is used to calibrate a simple phenomenological dislocation confinement model that rationalizes both the semi-invariant shape of the MC and the magnitude of hardening induced To shifts. The model hypothesizes that the local fracture properties, in this case treated as a critically stressed volume, depend on temperature in a way that is mediated by the overall alloy strength that controls crack tip dislocation structures. The simple model predictions compare favorably with the observed relation, ΔTo/Δσfl asymp; 0.7°C/MPa, where Δσfl is the change in the average flow stress between 0 and 10% plastic strain. A second focus is on synergistic hardening-non hardening embrittlement, where the latter is associated with weakening of grain boundaries by the helium accumulation that occurs in bulk quantities of greater than asymp; 500 appm, which is pertinent to fusion irradiation environments. It is shown that helium-hardening synergism and transition from cleavage to inter-granular fracture paths can lead to estimated To shifts in excess of 500°C. Approaches to managing helium in advanced nano-dispersion strengthened alloys are briefly described along with new fracture issues they raise.

The effect of strain rate on hydrogen embrittlement of low alloy 4340 steel was studied using double-notched tensile samples electrochemically charged in-situ with hydrogen in 1N H2SO4 + 5 mg/l As2O3 solution. The mechanical response of samples with prior austenitic grain sizes of 10 and 40 mu;m and martensitic hardness of 43-52 HRC were examined at, after hydrogen charging times of 0-20 min. For same hydrogen charging time increases in strain rate resulted in decreased failure strains and increased evidence of brittle fracture. Brittle fracture surfaces for the harder samples showed predominant intergranular fracture along the prior austenitic grain boundaries while their softer counterparts showed predominant cleavage fracture.

The effect of grain boundary hydrogen on the fracture behavior of nanocrystalline fcc materials was studied by atomistic simulation techniques. Tensile straining of polycrystalline Ni thin films with varying amounts of grain boundary hydrogen was simulated using molecular dynamics and EAM model potentials to strains of 15%. H content clearly affected the processes of nucleation and propagation of intergranular cracks. In samples with randomly placed hydrogen, it was observed that embrittlement occurs at hydrogen concentrations above roughly 4 atoms per square nm of grain boundary area. An increase in dislocation emission from the boundaries was also observed. The presence of hydrogen also influenced the various mechanisms of grain boundary accommodation of the strain.

We investigate how grain boundary (GB) network configurations affect macroscopic properties of polycrystalline materials using gallium permeability through GBs in aluminum as a case study.
Our in situ experiments show that gallium permeability proceeds non-uniformly through the aluminum GB network and that the penetration velocity is a function of GB crystallography and connectivity. The large statistics at our disposal allow us to generalize on the relations between GB character and mass transport through the microstructure of polycrystalline materials. Such knowledge aids the design of microstructures with desired aggregate properties through GB engineering.
This work was supported by the US Department of Energy, Office of Basic Energy Sciences under award No. DE-SC0008926.

This work concerns a study of the effects of plasticity on the mechanism of intergranular cracking assisted by hydrogen induced embrittlement in an aluminium alloy. Here, tensile specimens charged with hydrogen were used to investigate quantitatively the effect of plastic deformation on the mechanism of intergranular crack initiation at the scale of the individual grains. An experimental procedure was set up to monitor the evolution of surface strain fields on in-situ tested SEM notched specimens using digital image correlation techniques. In addition, measurements of the associated crystal orientation evolution at the micron scale were carried out using electron backscatter diffraction (EBSD). These measurements were then compared with finite element predictions of the local strain fields on the observed regions of the in-situ specimen. The numerical predictions were obtained using a dislocation mechanics-based crystal plasticity model to describe the constitutive behaviour of each individual grain. The crystallographic grain orientations of the region of interest were discretised for the finite element analyses from EBSD maps.
From this study, it was found that intergranular cracking due to hydrogen embrittlement in the Al alloy is locally triggered by high tensile grain boundary tractions, here estimated to be 170 ± 35 MPa. As importantly, the results also revealed that the conditions needed for grain boundary microcracks to initiate are greatly affected by the deformation of neighbouring grains: i.e. it was established that boundaries between two ‘‘hard&’&’ grains, inside a neighbourhood of ‘‘softer&’&’ deformed grains, are the first to fail. The implications of these findings to optimise grain boundary resistance to environmentally assisted cracking through the use of grain boundary engineering will be discussed.

First-principles calculations and interatomic potentials were used to assess various aspects of WC/WC grain boundary strength in WC-Co cemented carbides. With density functional theory (DFT), we have investigated the impact on the work of separation (with and without local rearrangement of atoms) arising from segregated transition metal atoms. For segregation in sub-monolayer proportions, we find a strengthening effect of Co atoms (as well as of Ni, Fe, and Mn), while the effect of carbide forming atoms is small (Ti, V, Cr, Zr, Nb, and Ta). At temperatures approaching the Co binder phase melting point, WC-Co shows a brittle to ductile transition where grain boundary sliding (GBS) is believed to become a relevant deformation mechanism. To understand how GBS contributes to this transition, we perform atomistic simulations of GBS at high temperature. For this purpose, we have used DFT calculations and experimental data to construct an interatomic potential of the Tersoff form for the W-C-Co system. The effect on sliding of segregated Co atoms and thin Co films of varying thickness was then investigated at 1500 K. This enables us to calculate limiting stresses for constant sliding rates. It is concluded that nanometer-thick Co films in the grain boundary significantly facilitate GBS, and that submonolayer segregation of Co increases the resistance to sliding.

The mechanical behavior of nanocrystalline materials, specifically their strength, greatly depends upon the strength of the grain boundaries (GBs). Hydrogen can be detrimental for grain boundary strength and trace amounts of interstitial hydrogen can potentially segregate to the GBs and be responsible for grain boundary fracture. In order to understand the mechanism of hydrogen (H) embrittlement in Aluminum, it is revealed through this work that, depending on the GB structure, the segregation and fracture energies of hydrogen at different interstitial positions could possibly vary. First-principles density functional theory based calculations were performed on sum;5(012)[100] symmetrical tilt boundary of Al with and without H segregation, to investigate the thermodynamics of H segregation induced embrittlement of Al. It is seen that H atoms potentially segregate at the grain boundary (GB) region of Al and lowers the GB strength to fracture. A number of stable and metastable interstitial sites for H were identified in and around GB and diffusion of hydrogen along different axes direction were examined. It was found that for sum;5 in Al, the most stable location of H interstitial is not exactly on the GB plane but out of GB plane. These interstitial locations provide fast diffusion channel (with significantly low diffusion barriers compared to bulk) across GB but disclose slower diffusion (with larger barrier) along GB. It was observed that the fracture energy of the interstitial sites can be related to the local coordination of the H atom and provide a volumetric effect towards the fracture of GB. The electronic structure analysis displays strong charge densities around H interstitial which weakens the neighboring Al-Al bonds in H segregated Al GB. Charge clustering observed for each of the high segregation energy sites can be the cause for the detrimental effect on the GB strength.

A crack in a material or structural component extends, if the crack driving force equals or exceeds the crack growth resistance. A material inhomogeneity or an inhomogeneous residual stress field can strongly diminish or enhance the crack driving force, e.g. [1]. This influence offers new possibilities for the design of new damage-tolerant and fracture-resistant materials: By introducing intentional material property variations at a certain wavelength, the crack driving force can become so low that a crack might stop to grow.
For the evaluation of the crack driving force in inhomogeneous materials, we have applied the concept of configurational forces [1,2]. Configurational forces are thermodynamic forces that determine the movement of defects in materials [3]. The crack propagation direction can be also evaluated with this concept, as well as the growth rate of cracks in cyclically loaded components [2]. The distribution of configurational forces in the materials and the crack driving force are evaluated by post-processing after a conventional finite element stress and strain analysis. From the results of the computations, it is tried to find “optimum configurations”, that is, to find for a given material a composite architecture so that the crack diving force exhibits a minimum [4].
The procedure will be demonstrated on various examples of monotonically and cyclically loaded composites. Materials with long and short cracks are considered. Experiments are conducted to validate the computational results [5].
References
[1] N.K. Simha, F.D. Fischer, O. Kolednik, C.R. Chen, Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials. Journal of the Mechanics and Physics of Solids 51 (2003) 209-240.
[2] O. Kolednik, J. Predan, F.D. Fischer, Reprint of “Cracks in inhomogeneous materials: Comprehensive assessment using the configurational forces concept”. Engineering Fracture Mechanics 77 (2010) 3611-3624.
[3] M.E. Gurtin, Configurational forces as basic concepts of continuum physics. Springer, New York, 2000.
[4] O. Kolednik, J. Predan, F.D. Fischer and P. Fratzl, Bioinspired design criteria for damage-resistant materials with periodically varying microstructure. Advanced Functional Materials 21 (2011) 3634-3641.
[5] J. Zechner, O. Kolednik, Fracture resistance of aluminum multilayer composites. Engineering Fracture Mechanics, in press.

We describe measurements of the lower bound on the total density of Geometrically Necessary Dislocations (GND) on individual slip systems of a nickel crystal indented by a wedge. The GND content is measured by high-resolution electron backscatter diffraction (EBSD) with spatial resolutions of 2500 nm, 500 nm, 200 nm, 100 nm, and 50 nm. The multiple length scale measurements demonstrate that the GND density varies quasiperiodically, and the period of the GND variation is a characteristic length scale of crystal plasticity. Since the physical consequence of the formation of the quasiperiodic GND dislocation structure is to limit the mobility of dislocations, the dislocation mean free path length is assumed to scale with the period of the varying GND density. We demonstrate that the dislocation mean free path length becomes shorter as deformation proceeds in a well-defined way. In addition, we demonstrate that there is a distribution of the dislocation free path length and describe measurements of the range. Finally we consider the evolution and self-organization of the GND dislocation structures as deformation proceeds.

Adiabatic shear failure is a dynamic failure mechanism that has been extensively investigated since the early 1940&’s. The prevailing assumption is that thermal softening plays a dominant role as a destabilizing factor leading to the formation of localized shear surfaces, referred to as adiabatic shear bands (ASB). Considered as an instability, the phenomenon has been quite successfully modeled using perturbation analysis which leads to the prediction of a critical failure strain.
In the recent years, we have re-examined the prevailing assumption of a dominant thermal softening from an experimental point of view, showing that for a sufficiently large number of materials studied, thermal excursions are of a quite limited extent for several alloys that indeed fail by ASB, but at relatively small strains, such as Ti6Al4Vand maraging steel among others. This observation has led to the identification of a critical value of the strain energy (density), with emphasis on its athermal component, the so-called stored energy of cold work (SECW). This parameter is particularly attractive as it ties smoothly the mechanics of ASB formation and its physics through microstructural evolutions.
In this presentation, we will review some of the more important results in this subject, related to the measurement and rate-dependence of this critical value of the SECW. Emphasis will be put on the identification and the interplay between the 2 main deformation mechanisms, namely dislocations slip and twinning. A fully coupled numerical model, in which the microstructural evolutions are included, will be described. This model can be used to differentiate microstructural from thermal softening, and the contribution of each mechanism.
The main outcome of this work is that, whereas perturbation analyses are quite adequate to represent ASB formation, we suggest that the perturbation should not solely concentrate on thermal fields and associated softening effects, but also consider softening microstructural evolutions to provide a more complete picture.

Experimental results showing the development of twins and cleavage cracks in Zinc grains in galvanized steel sheets and kink banding at the crack tip in nickel base single crystal superalloys will be reported [1,2,3]. The usual continuum crystal plasticity framework is extended to incorporate twinning and cleavage phenomena so as to explicitly simulate the nucleation and development of twins in single crystals. As an example, simulations of the formation of twins at a crack tip in Zinc thin films will be presented and compared to the experimental observations.
The competition of slip and kink band formation will also be simulated, including the lattice curvature that arises in the presence of kinks [4]. Finally the crystal plasticity model is extended to include cleavage fracture using a continuum damage model incorporating the effect of normal stress
on the cleavage plane and accumulated plastic slip. The general framework including a micromorphic regularization method is then suitable for the finite element simulation of crack propagation in single
crystals [5].
[1] R. Parisot, S. Forest, A. Pineau, F. Nguyen, X. Demonet and J.-M. Mataigne, Deformation and Damage Mechanisms of Zinc Coatings on Galvanized Steel Sheets, Part I: Deformation Modes , Metallurgical and Materials Transactions, vol. 35A, pp. 797-811, 2004.
[2] R. Parisot, S. Forest, A. Pineau, F. Grillon, X. Demonet and J.-M. Mataigne, Deformation and Damage Mechanisms of Zinc Coatings on Galvanized Steel Sheets, Part II: Damage Modes , Metallurgical and Materials Transactions, vol. 35A, pp. 813-823, 2004.
[3] S. Flouriot, S. Forest, G. Cailletaud, A. Koster, L. Remy, B. Burgardt, V. Gros, S. Mosset and J. Delautre, Strain localization at the crack tip in single crystal CT specimens under monotonous loading : 3D Finite Element Analyses and Application to Nickel-Base Superalloys , Int. J. Fracture, vol. 124, pp. 43-77, 2003.
[4] S. Forest, P. Boubidi and R. Sievert, Strain Localization Patterns at a Crack Tip in Generalized Single Crystal Plasticity , Scripta Materialia, vol. 44, pp. 953-958, 2001.
[5] O. Aslan, S. Quilici and S. Forest, Numerical Modeling of Fatigue Crack Growth in Single Crystals Based on Microdamage Theory , International Journal of Damage Mechanics, vol. 20, pp. 681-705, 2011.
[6] O. Aslan, N.M. Cordero, A. Gaubert, S. Forest, Micromorphic approach to single crystal plasticity and damage , International Journal of Engineering Science, vol. 49, pp. 1311--1325, 2011.

In this study, a yield function able to represent the behavior of single crystals containing voids is proposed. Its derivation is based on a variational approach which is modified to match the stress state dependence obtained for the Gurson model. Three adjustable parameters are introduced which are fitted on unit cell finite element calculations performed for various stress triaxiality ratios, main loading directions and porosity levels in the case of a perfectly plastic FCC single crystal. A very good agreement is obtained. The model can possibly be applied to describe failure of irradiated stainless steels when the irradiation doses are high enough to create very small cavities (10-50 nm) inside grains.

Recently, the exciting new research field on the mechanical behavior of nanotwinned metals was opened up. These nanotwinned metals have strength comparable to advanced structural materials (i.e., high-strength steels, composites or nanocrystalline metals). Moreover nanotwinned metals typically show a more pronounced ductility compared to their nanocrystalline counterparts. However, previous studies have revealed that cyclic loading can lead to detwinning causing cyclic softening. It is also known that partial and full dislocation interactions with coherent and incoherent twin boundaries in their microstructures play a significant role in such microstructural changes (i.e., twinning and detwinning) during cyclic deformation. These previous studies focused mostly on cyclic loading with a fairly small number of cycles. Here novel cyclic bending tests with cycle numbers of up to 10^7 were performed on free standing cantilevers of epitaxially grown, nanotwinned 20µm-thick Cu (111) films. During bending tests, the strain varies along the beam axis as well as through film thickness, and thus such a loading condition allows us to probe microstructural evolution as a function of strain in one test. After high cycle fatigue tests, the accumulated damage at film surface and the detwinned microstructure within subsurface layers were systematically investigated by using serial cross-sectioning, nanoindentation, and transmission electron microscopy. These results are discussed to reveal detwinning mechanisms in nanotwinned structures under cyclic bending condition.

The purpose of this contribution was to characterize ductile damage in Dual-Phase steels and obtain quantitative data concerning the damage nucleation, the void growth and the coalescence. This data was then used to develop or validate analytic models concerning every steps of damage. The main contributions are described below.
- Quantitative data concerning every steps of ductile damage was obtained using X-ray tomography. The void nucleation was characterized using the number of cavities present in the studied volume, the void growth using the equivalent diameter and the main dimensions of the twenty largest voids of the volume and the void coalescence using the distance between cavities. For the first time, void coalescence was experimentally and quantitatively characterized in an industrial steel.
- The quantitative data concerning the void nucleation was employed to develop a modeling predicting the kinetic of void nucleation in the studied steels either based on a stress criterion of decohesion or based on a strain criterion of particle fracture, depending on the observed nucleation mechanism. The ferrite / martensite interface stress of the studied DP steel was estimated using this prediction.
- By using the quantitative measurements on the void growth performed on several notched specimens, the Huang&’s correction of the void growth model of Rice and Tracey, which better takes into account the effect of triaxiality, was experimentally validated. The use of this model also showed that microstructural parameters not taken into account in this simple model, in particular the yield stress of the material, have an influence on the growth of cavities.
- For the first time, the Brown and Embury criterion and the Thomason criterion were experimentally tested on the strained specimen. Both criteria were locally applied on every couples of neighbouring voids. This local approach showed that the Thomason criterion was the most adapted to predict the local events of coalescence.

Ductile fracture is a field in which Andre Pineau has made many contributions. It is far from being closed. A number of open questions related to ductile fracture will be examined in this contribution: situations where it is expected to occur and doesn&’t (such as high-temperature cleavage of Aluminum alloys), situations where it is expected to occur and is prevented to (such as fracture of fcc materials under irradiation), situations where it occurs in a graded microstructure (such as ductile fractures in welds), situations where the initiation depends strongly on the contrast between phases (like in metal ceramic composites), situations where it depends strongly on the detailed microstructural features (like in dual phase materials).

Four litigations are briefly described showing how scientific enquiry can be in conflict with litigation procedures. Popper's "Objective Knowledge" inspires the bases of a sound scientific investigation of an accident. Often a few court experts simply ignore them. The first example is the fracture of a large cast iron water pipe wrongly attributed to contact with a concrete cable duct, which supposedly had increased locally the stresses in the wall. Calculations showed that this was not the case. The second example is a concrete water pipe which presumably failed because, following the installation of telephone wires, the trench had not been properly filled, leaving a cavity under the water pipe. Its fracture resistance in bending was wrongly estimated. It could be demonstrated that the applied load was insufficient to break it. The third example is the fracture of a large gear reducer during an overspeed test. A laboratory had concluded from fractography that fatigue was the reason of the failure, simply impossible since no cyclic load had ever been applied. The fourth example is the accident of the Pic de Bure cable car due to gliding of the haul rope grip. It was a new device, which had never been tested. The design calculations had ignored the laws of friction. In spite of this deficiency the manufacturer was not even summoned.

We use high-energy diffraction microscopy (HEDM) and X-ray absorption tomography (XRAT) to reconstruct the 3D microstructure of a nickel-base superalloy specimen that has been fractured in a hydrogen (H) environment. HEDM and XRAT are nondestructive techniques that are capable of characterizing crack morphologies and grain boundary (GB) networks. We focus on locating crack bridging ligaments and characterizing the crystallography of the grains within these ligaments. Then, we perform molecular dynamics (MD) simulations of fracture of these GBs in presence of hydrogen. Using these simulations, we hope to elucidate the detailed atomic-level fracture mechanisms, especially the effect of GB structure on fracture in the presence of hydrogen.
This work was supported by the BP-MIT Corrosion and Materials Center.

Adiabatic shear band (ASB) formation is of practical and scientific interest. This mode of deformation is associated with intense strain localization, extremely high localized temperatures and frequently with low energy fracture, especially in high strain rate applications. Tresca first reported intense localized heating when a billet of Pt-Ir alloy was hammered just below visible red heat; red heat lines in the form of an “X” were observed along the “lines of maximum sliding”. Later work by Basinski on Al and Al alloys with low heat capacities at low temperature revealed: (1) the stress strain curves showed large load drops, (2) deformation took place by dislocation glide, (3) deformation was localized around the fracture surface and was probably associated with an avalanche of dislocations, (4) considerable heating of the bulk material was associated with the load drops, (5) more nearly adiabatic conditions resulted in an increase in the frequency of load drops and (6) load drops formed only when the physical properties of the material promoted a high degree of localized heating. Eshelby and Pratt examined the temperature increase for evenly spaced dislocations moving past at a point and concluded that this could not account for large temperature increases nor was there any dislocation configuration that could account for more than a few degrees of localized heating. However, the conclusions drawn by Eshelby and Pratt disagree with a wealth of observations which point to high localized heating. Armstrong and colleagues modified the above approach by assuming that the critical event in ASB formation and localized heating was the collapse of a dislocation pile-up. Using an upper limit for the dislocation velocity of the shear wave speed and with other parameters for steel, a temperature increase of 3200K was obtained. The over-estimated temperature rise for pile-up collapse was taken to give credence to the proposed mechanism. High rate deformation of Ti-6Al-4V showed melted regions lending credence to the pile-up collapse mechanism. A simplification of the slip band collapse (SBC) model is presented which includes pertinent microstructural factors. The physical basis of SBC is easily understood in terms of the difference in energy of a pile-up of n dislocations and a collapsed slip band (i.e. n discrete, non-interacting dislocations) which is used to compute the adiabatic temperature increase. Using literature data a temperature increase of about 1000K was computed, in agreement with numerous observations of localized heating in steels and in essential agreement with the SBC model. It is suggested that the simplified model may be used to obtain first order estimates of the temperature increase and consequently predict the tendency towards low energy fracture, taking into account microstructural and thermal properties.

Bulk-metallic glass alloys (BMGs) make promising candidates for many structural applications principally due to their high strength and ease of processing. However, as strength and toughness are generally mutually exclusive, early glasses presented a challenge with low toughness values and disappointing fatigue strengths. Early measurements of toughness were compromised by single shear-band failure at near-zero tensile strains, and fatigue strengths were so low that 10⁷-cycle fatigue limits approached a mere 0.04 UTS, a fact attributed to the lack of microstructure with no features to locally arrest incipient cracks. BMG-matrix composites have overcome this limitation by introducing crystalline second-phase dendrites to arrest shear-band cracks before they exceed critical size resulting in fracture toughnesses in excess of 100 MParadic;m and fatigue limits of ~0.3 UTS. In the absence of a second phase, however, one might ask whether such fracture and fatigue properties are also achievable in a monolithic glass? One approach is to promote the formation of multiple shear bands to effectively mimic plasticity but suppressing their cavitation into cracks. This can be achieved by increasing the bulk modulus at the expense of the shear modulus. Using this philosophy, a Pd-based monolithic glass was developed with strengths exceeding 1.5 GPa which shows fracture toughness values of ~200 MParadic;m and fatigue limits comparable with that in composite BMGs, making it one of the most damage-tolerant materials on record. The proliferation of shear bands appears to be primarily responsible for the high toughness, but this also has the benefit of inducing highly faceted crack surfaces in fatigue, which leads to high fatigue thresholds and fatigue limits. The mechanisms underlying such properties will be discussed and the results compared to latest advances in monolithic Zr-based glasses.

Twinning is one of the most prevalent deformation mechanism in HCP crystals. Recent experimental studies have suggested that twin nucleation during c-axis compression of Mg single crystals is size dependent. However, these studies have neglected the influence of the initial dislocation density in these crystals. To address this, in this study we perform large scale molecular dynamics simulations c-axis compression of Mg single crystals having different densities of per-existing dislocation network and crystal sizes varying between 20 and 100 nm in diameter. From these simulations two twin nucleation mechanisms are identified, namely, surface-induced twin nucleation, and dislocation-induced twin nucleation. The former dominates at low dislocation densities, while the latter dominates when there are sufficient dislocations in the sample such that appropriate dislocation junctions and dislocation reactions can lead to twin nucleation. At intermediate dislocation densities neither of these two twin nucleation mechanisms are likely to exist, and plastic deformation is solely accommodated by c+a dislocation slip.

An attempt to break a piece of brittle crystal like diamond usually terminates with two suddenly broken pieces. It is therefore commonly accepted that cracks in these materials are propagating, initially, at high speed. Over the last two decades, theoretical studies and atomistic computer calculations, 2D in nature, have been in accord with the common intuition, suggesting that the energy required to propagate cracks in brittle crystals is higher than the Griffith twice the free surface energy threshold and crack speed can&’t be lower than a correlated threshold. Contrary, our high resolution fracture experiments of silicon crystal show that cracks can propagate at very low speed provided the energy supply to the crack tip is low. Furthermore, our experiments show that cracks&’ front is curved. This fact is of fundamental importance, as it suggests that the front is constructed from enormous planar atomistic-scale steps, which set a new length scale in fracture and responsible to completely different energy barrier for crack initiation and mechanisms of crack propagation.
We, therefore, performed a new type of atomistic computer calculations of silicon like crystal containing a curved crack with different boundary conditions. These calculations show that cracks in brittle crystals can propagate at low speed at energy comparable to Griffith&’s theoretical threshold and at temperatures ~ 300K the energy-speed relationship obeys the continuum based Freund equation of motion. High resolution fracture experiments confirm the theoretical findings.

Nanoscale twinning is effective in enhancing both yield strength and tensile ductility, characteristics that are generally mutually exclusive in face-centered-cubic metals. Nanotwinned metals, however, prove to fail well below their theoretical strength limit due to heterogeneous dislocation nucleation from boundaries or surface imperfections. This talk will present a combined experimental-atomistic simulation study on the fracture of ultra-thin gold nanowires containing high densities of twins varying from 0.7 nm to 5.6 nm in size. We find a remarkable ductile-to-brittle transition with decreasing twin size, opposite to the behavior of metallic nanowires with lower-density twins reported so far. It is also found that ultrahigh-density twins (twin thickness < 2.8 nm) give rise to homogeneous dislocation nucleation and plastic shear localization, contrasting with the heterogeneous slip mechanism in single-crystalline or low-density-twinned nanowires. As a result of this transition, Au nanowires with angstrom-scaled twins (~ 0.7 nm) exhibit tensile strengths up to 3.12 GPa, very close to the ideal theoretical limit. This phenomenon therefore represents a new type of size effect in the fracture of low-dimensional metals.

The mechanical properties of commercial uv-cured acrylate adhesives were measured at ambient and cryogenic (120 K) temperatures. The amount of the adhesive studied was further constrained to ~ 1-nano-liter; a volume that is representative of the amount of material used in our application, and is also relevant to the assembly of components involving micron-sized structures.

The stress-strain behavior of bulk quantities of the commercial adhesives was measured at room temperature to calibrate the performance of our equipment. The measured properties matched the reported values. The stress-strain behavior was re-measured using smaller (0.1 to 1-nl) volumes of adhesive. The measured ultimate strength of the adhesives was 70- to 250-% of the bulk strength of the material. These values were repeatable for each material and the variability was associated with different acrylate formulations. The strain-to-failure behavior of the small-volume samples was markedly different from the behavior of larger samples with the same chemical formulation, with the small volumes exhibiting substantially greater strain before failure.
The mechanical properties of the adhesives changed substantially when the material was cooled to 120 K. The ultimate strength increased 4-fold and the fracture of the material involved the formation of discrete fracture planes that allowed the material to yield incrementally before failing catastrophically; the stress-strain behavior of these materials is presented with corroborating SEM images of the fractured surfaces. TEM images of the fractured surfaces and a chemical analysis of the adhesives&’ composition provide a microstructural-based explanation for this behavior based on the segmentation of the hard and soft phases of the acrylate within the small volume during the uv-curing process of hardening the material.
Acknowledgment
This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944, the University of Rochester, and the New York State Energy Research and Development Authority. The support of DOE does not constitute an endorsement by DOE of the views expressed in this article.

Fatigue, tensile and fracture mechanics properties of nanocrystalline materials are rare, because the available material volume is usually very small. Severe plastic deformation (SPD) is a new method to produce ultrafine grained or nanocrystalline materials in larger quantities. This enables us to determine the ductility and fracture toughness of these types of materials. High pressure torsion allows SPD of most metallic materials. Hence, it allows the transformation of the typical microcrystalline materials to an ultrafine or nanocrystalline state.
The large HPT equipment at our institute permits now to determine standard tension and fracture mechanic tests on a large variety of metals and alloys. The paper will give an overview of the obtained results in pure metals, alloys, and nanocomposites. Special attention will be devoted to the developed anisotropy of the fracture toughness, which is in some materials extremely pronounced.
The first part of the paper will be devoted to the structural evolution during SPD with the special focus on the grain shape and texture. The second part of the presentation will show how the grain shape affects strength, ductility and fracture toughness in different bcc, fcc and hcp metals and alloys.

Nanocrystalline metallic thin films are routinely used in a large range of applications, from hard coatings on bulk components to structural components in micro/nano electromechanical systems (MEMS/NEMS) and conductive layers in microelectronics devices. In all these applications, the nanocrystalline thin films undergo cyclic loading, either due to repeated surface contact, applied mechanical loading, or thermally-induced stresses. As such, the fatigue properties of this class of materials should be adequately characterized to ensure proper reliability of these components and devices. In addition, the underlying mechanisms should be understood so that fatigue resistant nanocrystalline thin films can be processed. This study investigates the cyclic plastic deformation properties and fatigue crack initiation mechanisms of nanocrystalline gold thin films using a novel quantitative in situ TEM MEMS-based tensile testing technique. The MEMS device provides both actuation and sensing of the specimen via electrical signals while TEM imaging provides information on the microstructure evolution during cyclic deformation. It comprises two identical capacitive sensors on each side of the specimen that are used to measure the specimen gap change and applied force with nanometer and micro newton precision, respectively. Appropriate calibration of the MEMS device and manipulation/clamping procedure of the nanocrystalline gold thin film specimens onto the MEMS device were developed to obtain accurate measurements of the specimens&’ mechanical properties, based on their measured elastic moduli. The tensile strength of the gold specimens (100 nm thick, 1 micron wide, ~5 micron long) is ~1.2 GPa with a total strain to failure of ~2.5 %. Preliminary quantitative in situ TEM tension-tension fatigue tests on nanocrystalline gold specimens with maximum applied stresses of ~1 GPa revealed fatigue cracks nucleation after 7000 cycles.

Rapid development of micro/nano-devices demands high-performance micro-components with long-term reliability. Fatigue of a metal at nanoscales is not only an important issue for the applications, but also a fundamental question needed to be elucidated. Recent investigations have shown that there is an evident difference in fatigue behaviors between thin metal films confined by substrates and their bulk counterparts due to the strong confinement of small geometrical and microstructural dimensions on dislocation motion. In this talk, we will present an experimental investigation of fatigue properties and damage behavior of nanocrystalline Au films with thickness ranging from several tens to hundreds of nanometers constrained by a flexible substrate. Our results show that the resistance to fatigue cracking increases with decreasing film thickness even at nanometer regime. Fatigue damage in the thicker film initiates from the place with well-developed strain localization, while that in the thinner film is associated with grain boundary-related behaviors, such as intergranular cracking, grain coarsening as well as deformation twinning. Such scale-dependent fatigue behaviors will be analyzed and the corresponding mechanisms are evaluated.

This work investigated the fatigue properties of electrodeposited Ni microelectromechanical system (MEMS) micro-resonators and the underlying size effects related to these micron-scale specimens. More specifically, the influence of stress amplitude, plastic strain amplitude, and environment on the high and very high cycle fatigue degradation of electrodeposited, 20-micron-thick Ni films was studied for several normalized values of extreme stress gradients (ranging from 8% to 36% per micron). The specimens have a columnar microstructure and are tested in fully-reversed bending at resonance (~8 kHz) in mild and harsh environments (30 °C, 50% relative humidity (RH), 80 °C, 90% RH, and 80 °C, 5% RH). The stress amplitudes range from 100 to over 600 MPa. Fatigue damage in the form of extrusions, micro-cracks, and surface oxidation was observed using scanning and transmission electron microscopy, and tracked using resonant frequency monitoring. Finite element modeling was also used to confirm the effects of these fatigue-related events on the device&’s resonant frequency. Only non-propagating cracks were observed for stress amplitudes as high as ~60% of the ultimate tensile strength after up to 4 billion cycles. This superior fatigue resistance is attributed to the extreme stress gradients specific to these micro-resonators. However, transmission electron microscopy of specimens fatigued for billions of cycles revealed highly localized thick surface oxides (up to 1100 nm) at the location of fatigue extrusions. The implications of these results on the governing fatigue crack nucleation mechanisms under these MEMS-relevant loading conditions will be discussed.

Fatigue damage of metal electrode on the soft substrate is one of the critical issues in flexible devices since electrical conductivity of metal films can degrade gradually because of fatigue crack generation. Here, we systematically investigated the electrical resistance change of the metal film on a polymer substrate during fatigue cycle. The resistivity changes after crack nucleation could be scaled using a dimensional analysis with respect to crack nucleation cycles, which indicates that controlling the crack nucleation would be crucial against fatigue damage. To suppress crack nucleation, we introduced a novel nanostructured fatigue damage-free copper electrode on flexible substrate by creating 2-D nanohole arrays. The arrayed nanoholes control the collective dislocation slips and decrease the average strain level so that electrical conductivity of nanohole-containing electrodes surprisingly maintained even under 500,000 bending cycles whereas that of untreated conventional copper increase by three times under the same condition.

Electrolytic hard chrome (EHC) coatings exhibit an attractive combination of properties including: low cost, high hardness, low coefficient of friction, good abrasive/sliding wear resistance and excellent corrosion resistance. These characteristics have led to EHC being used for a wide variety of metallic components such as: hydraulic and pneumatic piston rods and cylinders, actuators, pump shafts and rotors. The main drawbacks of EHC coatings are that the electro-plating process requires the use of toxic hexavalent chromium species and that there is a significant fatigue debit associated with the presence of the hard coating. As such, there has been a concerted effort within the surface finishing community to identify environmentally benign alternatives to EHC.
Recently there has been significant interest in nanostructured electrolytic coatings based on Ni-P or Co-P, which can be produced using much less toxic electrolytes. Such coatings exhibit high hardnesses, high yield strengths and excellent wear resistances. At low P contents nano-crystalline grains are formed when a combination of electro-deposition variables (current density, pH, temperature, and bath composition) are chosen that promote grain nucleation and inhibit grain growth (e.g. [1]). At high P contents, the atomic size difference between P and Co or Ni suppresses crystallization, and fully amorphous coatings can be produced [2]. Intermediate P contents lead to nano-composite microstructures comprising nano-crystalline regions embedded in an amorphous matrix. Recent work has shown that coatings with the latter structure exhibit particularly promising properties [3].
Here we describe a study on the low-cycle fatigue (LCF) behavior of AISI 4340 with nanostructured Co-P coatings. The influence of the coating on the nucleation of fatigue failure is deduced from fractographic analyses by scanning electron microscopy on coated and uncoated LCF specimens. This behavior is related to the variation in the microstructures and properties of the coatings with P content as determined by transmission electron microscopy and nanoindentation, respectively.
References
[1] U. Erb, K.T. Aust, G Palumbo, in Nanostructured Materials, 2nd Edition, Ed. C.C. Koch (William Andrew, Norwich, NY) (2006) 235.
[2] N. Lu, J. Cai, L. Li, Surf Coatings Tech 206 (2012) 4822.
[3] J. Carpenter, A. Kertesz, A. Datta, Adv Mater Proc 167 (2009) 25.

Using high resolution TEM, we show atomistic scaled fracture in Au nanowires containing angstrom-scaled twins (0.7 nm in thickness) which exhibits tensile strengths up to 3.1 GPa, near the ideal limit. A remarkable ductile-to-brittle transition with decreasing twin size, opposite to the behavior of metallic nanowires with lower-density twins reported so far. Ultrahigh-density twins (twin thickness < 2.8 nm) are shown to give rise to homogeneous dislocation nucleation and plastic shear localization, contrasting with the heterogeneous slip mechanism observed in single-crystalline or low-density-twinned nanowires.

Magnesium alloys have a high potential for application as structural materials because of being the lightest among all the structural alloys in use. To use the structural applications, the development of high strength and toughness magnesium alloy is important. Recent studies show that the grain refinement is one of the effective methods to improve not only the toughness but also the strength and ductility in magnesium and magnesium alloys. The dominant plastic deformation mechanism is also reported to change from twins to dislocation slip by the refinement of the grain structures; however, the detailed fracture mechanism in fine- and coarse-grained magnesium alloy has not been understood yet. In this study, the deformed microstructure of the fracture toughness tested fine- and coarse-grained magnesium alloy was investigated through experiments, i.e., microstructural observation, and simulations techniques. The present results show that the fracture mechanism changes from a brittle fracture on the account of the deformation twins to a ductile fracture associated with the void formation, and thus the fine-grained alloys have high fracture toughness resulting from the resistance to the twins at the beginning of the deformation.

A new in-situ TEM nanotensile testing method recently developed by Hysitron Inc. was combined with the Automated Crystallographic Orientation Indexation TEM (ACOM-TEM) technique in order to unravel the elementary mechanisms controlling the plasticity and the fracture of ultrafine-grained (ufg) <111> textured aluminum (Al) thin films. Electron beam evaporated Al freestanding thin films have been produced using microfabrication techniques based on MEMS-type procedures. Ex-situ TEM analysis on the as-deposited films shows that the microstructure consists of equiaxed ufg grains with a mean grain size of 342±17 nm. The grain size ranges from 100 nm to 1 micron making this system an ideal candidate to investigate both intergranular and intragranular small-scale plasticity mechanisms. The in-situ nanomechanical experiments combining bright-field TEM (BF-TEM) and ACOM-TEM were achieved in displacement controlled mode. The results show that, in contrast with standard in-situ TEM nanomechanical testing methods based mainly on diffraction contrast imaging, the coupling of these two techniques strongly improves the in-situ characterization of deformed ufg materials. A transition from grain rotation to dislocation starvation deformation mechanisms was observed at about 2% deformation of the Al films. Furthermore, several mechanisms have been revealed during the fracture of these films including twinning and local necking on individual grains. The effect of the observed mechanisms on the mechanical behavior of the Al films is discussed and compared to recent works in the literature.