Critical Strain Level Research Articles

A microelement plastic strain accumulation model for fatigue life prediction

In this article, we present a novel approach to fatigue life prediction based on a Jenkin–Masing model. The Jenkin–Masing model describes the mechanical response of a material through a large number of parallel microelements, which are taken to be elastic-perfectly plastic with different yield strengths. Even below the macroscopic yield of the material, plastic strain is accumulated in the weaker microelements during cyclic loading. These microelements are taken to fail when a critical level of plastic strain is accumulated in them. We study the monotonic response, cyclic behavior and fatigue life of this model. In particular, the model shows how different realizations of distributions of microelement strengths may show similar monotonic behavior but very different fatigue behavior. This model provides insight into the origin of the large scatter in fatigue life widely observed in experimental results.

The loading direction dramatically affects the mechanical properties of the mouse tibia.

Introduction: The in vivo tibial loading mouse model has been extensively used to evaluate bone adaptation in the tibia after mechanical loading treatment. However, there is a prevailing assumption that the load is applied axially to the tibia. The aim of this in silico study was to evaluate how much the apparent mechanical properties of the mouse tibia are affected by the loading direction, by using a validated micro-finite element (micro-FE) model of mice which have been ovariectomized and exposed to external mechanical loading over a two-week period. Methods: Longitudinal micro-computed tomography (micro-CT) images were taken of the tibiae of eleven ovariectomized mice at ages 18 and 20weeks. Six of the mice underwent a mechanical loading treatment at age 19weeks. Micro-FE models were generated, based on the segmented micro-CT images. Three models using unitary loads were linearly combined to simulate a range of loading directions, generated as a function of the angle from the inferior-superior axis (θ, 0°-30° range, 5° steps) and the angle from the anterior-posterior axis (ϕ, 0°: anterior axis, positive anticlockwise, 0°-355° range, 5° steps). The minimum principal strain was calculated and used to estimate the failure load, by linearly scaling the strain until 10% of the nodes reached the critical strain level of -14,420με. The apparent bone stiffness was calculated as the ratio between the axial applied force and the average displacement along the longitudinal direction, for the loaded nodes. Results: The results demonstrated a high sensitivity of the mouse tibia to the loading direction across all groups and time points. Higher failure loads were found for several loading directions (θ = 10°, ϕ 205°-210°) than for the nominal axial case (θ = 0°, ϕ = 0°), highlighting adaptation of the bone for loading directions far from the nominal axial one. Conclusion: These results suggest that in studies which use mouse tibia, the loading direction can significantly impact the failure load. Thus, the magnitude and direction of the applied load should be well controlled during the experiments.

Post-buckling development in soft particulate composites

In this paper, we investigate the post-buckling development of instability-induced patterns in soft particulate composites. Upon reaching the critical strain level, the composite experiences microstructural buckling. Interestingly, in the post-buckling regime, the initial buckling mode may evolve into different new patterns. These transformations are governed by the initial microstructure parameters. In particular, depending on the initial distance between the columns of inclusions, the initial instabilities may develop into (i) inclusion chains with a zigzag or wavy shapes, (ii) a combination of inclusion sets in different length scales, (iii) seemingly disordered inclusion sets, (iv) and structures with strictly doubled periodicity. The different post-buckling patterns are further characterized via the discrete Fourier transform (DFT) analysis. Our results also show that the initially formed post-buckling patterns can further evolve into rather complex new shapes beyond a simple amplification in deformation.

Towards understanding the role of viscoelasticity in microstructural buckling in soft particulate composites

This work investigates the interplay between viscoelasticity and instabilities in soft particulate composites undergoing finite deformation. The composite is subjected to in-plane deformation at various constant strain rates, and experiences microstructural buckling upon exceeding the critical strain level. We characterize the dependence of the critical strain and wavelength on the applied strain rate through our numerical analysis.In the simulations, we employ the single and multiple-branch visco-hyperelastic models. We find that the critical strain and wavelength – characterized by the single-branch model – show a non-monotonic dependence on the strain rate, reaching a maximum at a specific strain rate. Remarkably, different buckling patterns (with different critical wavelengths) can be activated by changing strain rates. The space of admissible buckling modes widens in composites with higher instantaneous shear modulus. In the composites characterized by the multiple-branch model, the critical strain function exhibit multiple local maxima following a superposition of the single-branch responses. Typically, the branch with a larger relaxation time has a more significant effect on the critical strain. Moreover, the local maximum (of the critical strain function) is amplified by increasing the strain–energy factor of the corresponding branch term.Finally, we perform the experiments on the 3D-printed particulate soft composite characterized by a broad spectrum of relaxation times. The comparison of the experimental and simulation results demonstrates the ability of the numerical model to predict the critical buckling characteristics.

Localization in a plastically anisotropic void-sheet

Pre-existing voids distributed as a single, but inclined layer are used to represent material defects leading to void growth and strain localization in a sheet. Small elastic but finite plastic strain deformations are accounted for in an elastic-plastically anisotropic material hardening three-dimensional finite element framework. Localization is here defined as the stage of deformation, where the straining in the layer relative to the overall prescribed straining grows to infinity, i.e 104 or higher. Three different materials are consider using the classical Hill-48 anisotropic yield surface (Hill, 1948). As a reference case, one of them is the isotropic Mises case, whereas the other two are anisotropic cases. Yield surfaces and Lankfords coefficients are provided for all three materials. For each material two different void volume fractions and several different loading triaxialities as well as void band inclinations are presented and compared. The strain for localization is given and corresponding deformed void band orientations are discussed. Qualitatively, the responses of the two anisotropic sheets are similar to that of the isotropic Mises case: A minimum in strain at a distinct initial void-band orientation can be identified. Except for one case, all cases studied here result in a simple shift of the critical strain level at localization. However, under uniaxial plane strain tension the isotropic and anisotropic sheet localizes at almost the same value of straining.

Acoustic Emission Damage Detection during Three-Point Bend Testing of Short Glass Fiber Reinforced Composite Panels: Integrity Assessment

In this study, an acoustic emission (AE) technique was used as a passive non-destructive tool to detect the damage progress in short glass fiber-reinforced composite panels. AE detection was conducted during three-point bend tests, thus illustrating the flexural damage accumulation for composite panels with different sizes and fiber volume content. To demonstrate the universality of the employed integrity assessment methodology, AE data was detected using different timing parameters and two different transducer types, i.e., medium-band and wide-band frequency sensors. The AE waveform classification presented in this study is based on peak frequency distributions. Frequency bands that are associated with certain failure mechanisms, including matrix micro-cracking, fiber debonding, delamination, and fiber breakage, were obtained from the technical literature. Through this investigation, the concept of cumulative signal strength (CSS) and cumulative rise time versus peak amplitude ratio (CRA) as AE output parameters are shown to facilitate integrity assessment for the employed complex composite material system. Significant jumps in CSS and CRA curves could be correlated to critical strain levels and distinct damage events in the composite panels subjected to flexural loading.

Predicting damage evolution in panel paintings with machine learning

Understanding the mechanical behavior and properties of works of art, such as panel paintings, is helpful for evaluating the failure mechanisms in play, especially during exhibitions in confined spaces. A panel painting is typically formed by a wooden panel and by layers of gesso, followed by paints and varnishes on the top. Induced by environmental changes, the mismatch in the moisture response of a stiff gesso layer and of the underlying wood panel produces risk of fracture in the pictorial layer. This happens because the gesso layer experiences tension which leads to cracking if the mechanical strain exceeds a critical level. The proposed contribution aims to develop a 3D simplified model for paintings, to detect the environmental conditions which may lead to exceeding the critical strain levels. To this aim, a penny-shaped crack has been simulated inside the gesso layer, centered along the symmetrical planes. To establish if the crack is in critical conditions, the failure criterion of the strain energy density (SED) method has been used: when the critical SED value is reached, the crack is assumed to be in unsafe conditions, otherwise it is in safe conditions. Several combinations of the geometric parameters describing the model have been checked, allowing to define whether the different conditions are likely to lead to a further damage development. Finally, the obtained results have been used to train a preliminary extreme gradient boosting machine (XGBoost) that may be able to classify and predict the two possible outcomes: safe and unsafe. This way, by exploiting the capabilities of machine learning, it could be possible to limit the need of numerical simulations and to introduce new rationales in the framework of work of arts conservation.

Semianalytical Analysis of Overexcavation and Critical Support Pressure for Support Design in TBM Tunneling through Squeezing Rock Condition

Support damage is a typical hazard scenario associated with tunnel boring machine (TBM) drives in the squeezing rock condition. The stress release of the rock mass and the improvement of the support capacity are two effective methods to prevent support damage. The stress in the rock mass can be released by allowing a certain amount of overexcavation. The support capacity can be evaluated by solving the required support pressures corresponding to different critical strain levels. This paper aims to achieve a better understanding of preventing support damage for TBMs in the squeezing condition by quantitatively analyzing the overexcavation and the required support pressure. A semianalytical solution of the ground reaction curve is obtained. A simplified method of solving the support pressure with specific rock displacement is proposed. Based on the two solutions, the procedures for solving for the overexcavation and the critical support pressure are presented. Corresponding to the critical strain levels of 1%, 2.5%, 5%, and 10%, the response surfaces for critical support pressures in relation to the Geological Survey Index (GSI) and in situ stress are obtained via the nonlinear regression method. The influences of GSI, in situ stress, and the mechanical parameters of the concrete lining and shield on the size of the overexcavation are comprehensively investigated. A method to guide support design in the squeezing rock mass is proposed. Three tunnel cases are presented to demonstrate the application of the method, and three case histories that encounter support failures are discussed to illustrate the appropriate design measures through the proposed method.

The role of lamina cribrosa tissue stiffness and fibrosis as fundamental biomechanical drivers of pathological glaucoma cupping.

The primary biomechanical driver of pathological glaucomatous cupping remains unknown. Finite element modeling indicates that stress and strain play key roles. In this article, primarily a review, we utilize known biomechanical data and currently unpublished results from our lab to propose a three-stage, tissue stiffness-based model to explain glaucomatous cupping occurring at variable levels of translaminar pressure (TLP). In stage 1, a short-term increase in TLP gradient induces a transient increase in lamina cribrosa (LC) strain. Beyond a critical level of strain, the tissue stiffness rises steeply provoking cellular responses via integrin-mediated mechanotransduction. This early mechanoprotective cellular contraction reduces strain, which reduces tissue stiffness by return of the posteriorly deflected LC to baseline. In stage 2 a prolonged period of TLP increase elicits extracellular matrix (ECM) production leading to fibrosis, increasing baseline tissue stiffness and strain and diminishing the contractile ability/ability to return to the baseline LC position. This is supported by our three-dimensional collagen contraction assays, which show significantly reduced capacity to contract in glaucoma compared with normal LC cells. Second, 15% cyclic strain in LC cells over 24 h elicits a typical increase in ECM profibrotic genes in normal LC cells but a highly blunted response in glaucoma LC cells. Stage 3 is characterized by persistent fibrosis causing further stiffening and inducing a feed-forward ECM production cycle. Repeated cycles of increased strain and stiffness with profibrotic ECM deposition prevent optic nerve head (ONH) recoil from the new deflected position. This incremental maladaptive modeling leads to pathological ONH cupping.

Energy-based mechanistic approach for crack growth characterization of asphalt binder

The cohesive cracking within asphalt binders has a significant influence on fatigue cracking resistance of asphalt pavements. To more clearly understand the mechanism and accurately characterize the process of the cohesive cracking occurring within the asphalt binder, an energy-based mechanistic (EBM) approach is applied to determine crack length and the pseudo J-integral is adopted to calculate crack growth rate in this study. First, a critical strain level separating nonlinear viscoelasticity from damage is determined based on a statistical analysis approach, and the result indicates that 0.7% is a critical nonlinear strain level for unmodified asphalt binder. Then, the crack length of asphalt binders is derived based on a torque equilibrium equation and two energy balance equations, as well as crack length is measured and verified based on an image processing method. It is found that contact regions in cracked area of the asphalt binder are formed when performing a strain-controlled rotational shear load. The contact regions have two stages, which first increase to the peak and then decrease with the increase of loading time. Next, the crack growth rate is formulated based on the pseudo J-integral Paris’ law equation considering nonlinear viscoelasticity. A linear relationship between the crack growth rate and the function of material properties (such as shear modulus, phase angle) in double logarithmic scales is proven and experimentally verified. In addition, the Paris’ law parameters (n and A) associated with crack growth rate are determined. Results show that they are independent on strain levels and temperatures. For example, six values of n of the unmodified asphalt binder are approximately equal to 1.10 at 5%, 6%, 7% strain levels when test temperatures are 15°C and 20°C. They are inherent material properties for the asphalt binder.

Fatigue resistance of aged asphalt binders: An investigation of different analytical methods in linear amplitude sweep test

This paper aims to investigate the fatigue resistance of asphalt binders using different analytical methods and fatigue failure criteria with the consideration of various aging conditions. Four different performance grade (PG) binders with and without modifiers were tested by Linear Amplitude Sweep (LAS) test to characterize their fatigue behavior. The fatigue failure strain was determined using three different definitions: peak value of shear stress, peak value of phase angle and the maximum stored pseudo-strain energy. The damage characteristic curves and fatigue life were obtained by two kinds of analytical methods: dissipated energy-based method and pseudo-strain energy-based method. Statistical analysis shows that there is no distinct difference between these three criteria of fatigue failure for aged and unaged asphalt binders. However, for the modified asphalt binders at unaged condition, it is hard to observe the peak value of phase angle or stored pseudo-strain energy. The fatigue life determined by the pseudo-strain energy-based method is slightly higher than that of dissipated energy-based method across the entire loading strain range. In addition, the fatigue resistance of neat asphalt binder tested in this paper is deteriorated at high strain levels but improved at low strain levels and the critical strain level is approximate 4.5%. The effect of aging is asphalt specific and depends on the strain levels from the experimental results.

Unveiling damage mechanisms of chromium-coated zirconium-based fuel claddings by coupling digital image correlation and acoustic emission

Coated nuclear fuel claddings offer a promising, near-term solution to address the demand for next-generation, accident-tolerant fuel systems. It is expected that they will possess superior mechanical properties and greater oxidation resistance compared to current cladding technology, allowing for improved performance during beyond design-basis accident conditions. Here, we present a methodology to determine the failure mechanisms of chromium-coated zirconium-alloy claddings under expected, critical loading conditions. Three-dimensional digital image correlation and acoustic emission techniques were used in situ to monitor spatial strain and crack development of the claddings under two key, de-coupled loading conditions: expanding plug and four-point bending. Critical strain levels, at which cracking initiated, were determined to be 0.4% εhoop and 0.4% εxx for expanding plug and four-point bending, respectively. A two-dimensional fracture model was also developed for the expanding plug loading condition based on inputs determined from mechanical testing. It was concluded that coating fracture of expanding plug specimens was axisymmetric across the specimen circumference and occurred rapidly through the thickness of the chromium coating. Subsequent high temperature steam oxidation experiments on tested (cracked) expanding plug specimens showed no signs of oxidation degradation to the underlying zirconium alloy, thereby showcasing the effectiveness of the chromium coating. This comprehensive, multi-scale study is intended to inform future testing of next-generation, coated claddings and identify the resulting failure mechanisms that arise in beyond design basis accident conditions.

Buckling-induced band-gap modulation in zigzag carbon nanotubes

The alteration of the electronic band gap induced by axial compression of single-wall carbon nanotubes was investigated using molecular dynamics simulation. Beyond a critical level of compressive strain, three classes of buckling modes take place depending on the aspect ratio of the system. Among these three classes, two different shell-buckling modes are found to yield contrasting band-gap modulation behavior as a response to axial compression near the buckling threshold. The potential advantage of using shell buckling to induce gap modulations when designing nanotube-based electromechanical devices is also discussed.

Experimental study of the size effect on transverse cracking in cross-ply laminates and comparison with the main theoretical models

Transverse cracking of off-axis plies is typically the first step of some failure mechanisms in long fiber reinforced laminated composites. It is well known that the off-axis ply thickness affects strongly the strain level which this ply is able to withstand without cracking. Experimental evidences show that this critical strain level increases strongly with decreasing ply thickness for the thinnest plies, confirming a clear size effect. This fact could be used to inhibit transverse cracking with the use of the recently developed ultra-thin plies. However the classical failure criteria for composites are not able to predict this size effect. From the first tests in the 1970s, several models with very different hypotheses were proposed to predict this size effect. Surprisingly there is still not a clear consensus in the scientific community about which is the adequate model, though their fundamentals are radically different. In this work an extensive test campaign is carried out on self-similar [0/90]s cross-ply laminates of AS4/8552 carbon/epoxy. The size effect is evaluated spanning a broader spectrum of thicknesses than in the tests presented in the literature until now, in order to explore the range of thicknesses where the differences between predictions of the main theoretical models are larger. In spite of the inherent dispersion in the experimental results, the comparison shows that the purely stress-based criteria underestimates the apparent strength of the off-axis ply. The other models predict very similar results, particularly for the thinnest laminates, with slight underestimations or overestimations, depending on the model.

Numerical simulations of adiabatic shear localization in textured FCC metal based on crystal plasticity finite element method

Experimental investigations of adiabatic shear localization in the nanostructured face-centered-cubic (FCC) alloys have revealed that micro-texture has a key role in advancing the formation of adiabatic shear bands (ASBs) (see reference [35]). In this work, we present the crystal plasticity finite element simulations (CPFEM) of dynamic uniaxial compression and simple shear in polycrystalline models with different initial textures. The aim is to study the effects of typical textures, which are often observed in FCC metals after severe plastic deformation or recrystallization, on the formation of ASBs under high strain rate loading. The materials response is described by an elastic-viscoplastic continuum slip constitutive relation, in which the dependence of slip systems’ resistance on the temperature evolution is also considered. Simulation results show that, under high-rate compression, except for some textures which are not favorable for the formation of ASBs, different textures lead to various orientation of shear bands and different critical strains at which the shear localizations occur. High-rate simple shear loading is found to facilitate ASB formation. Even in the texture-free, namely Random texture, model obvious shear localization was observed. However, the dependence of slip system activation on texture leads to considerable variation in the critical shear strain level for ASB initiation. Additionally, the effects of some factors, such as strain rate, temperature rise and strength of materials, on the formation of ASBs in FCC textured metals are discussed to interpret the formation process in more depth. We also combined the experimental observations and numerical simulations to elaborate the reason why ASBs have rarely been reported in FCC materials.

Microstructural Control of Physical Properties During Deformation of Porous Limestone

AbstractWe performed triaxial deformation experiments in Purbeck limestone (13.8% average porosity) across the brittle‐ductile transition and monitored the evolution of permeability and wave velocities as a function of strain. In the brittle regime, the rock yields in dilation. In the ductile regime, the rock first yields in compaction and then undergoes net dilation at some critical level of strain. The permeability increases after failure in the brittle regime and decreases with increasing compaction in the ductile regime. The wave velocities decrease with increasing strain, and the material becomes transversely isotropic. At axial strains of the order of 5%, the anisotropy parameters (from Thomsen, 1986) are around ε ≈ −0.2 and δ ≈ decrease with increasing axial strain beyond the yield point−0.3. Under hydrostatic conditions, the rock also yields in compaction. The hydrostatic yield point is not marked by any significant drop or increase in wave velocity during loading, but wave velocities decrease (and therefore crack density increases) significantly upon unloading. In all our tests, the permeability change is proportional to the initial porosity change until the point of net dilation is reached. The strain at that point also acts as a scaling factor for the relative drop in P and S wave velocities during deformation. All our experimental data point to a disconnection between the evolution of permeability, porosity, and wave velocities during deformation in the ductile regime: permeability is controlled by a fraction of the micropore network, while wave velocities are mostly influenced by microcracks that do not contribute significantly to either the total rock porosity or fluid flow properties.

Prediction of critical strains and critical support pressures for circular tunnel excavated in strain-softening rock mass

The critical strain is a strain level at the tunnel periphery beyond which the instability and squeezing problems are likely to occur, thereby it provides helpful guide to assess the tunnel stability. Among the current studies for predicting the critical strain, the influence factors such as the required support pressure, the strain-softening behaviour of the rock mass, and the in-situ stress condition have not been comprehensively considered. This paper aims to overcome the limitation by proposing an improved tunnel critical strain classification, which consists of five typical critical strains and critical support pressures. Specifically, two critical levels correspond to the occurrences of the plastic softening and residual zones of the strain-softening rock mass at the tunnel periphery. Three tunnel strains of 2.5%, 5%, and 10% represent the squeezing potentials of the rock mass. The correlations between the input geological parameters and the geological strength index GSI are proposed on the basis of the existing empirical equations. A numerical procedure is presented to solve the five critical strains and critical support pressures. According to a large amount of the calculation result, the response surfaces for the critical support pressures in relation to the GSI and in-situ stress are obtained by the nonlinear regression method. The obtained critical strains are compared with the critical strain levels and measured tunnel strains by the current studies. The results indicate that, the reason for the unexpected secure condition with the large deformation in the rock mass can be attributed to the non-existence of the plastic residual zone; as the rock mass strength improves, the critical strain level reveals an unexpected growth, which is correlative to the considerations of the in-situ stress condition and the strain-softening behaviour of the rock mass.

An Experimental Investigation of the Size Effects in Forming Processes of High-Purity Thin Metallic Sheets

Miniaturization of small metallic systems can lead to a softening of the mechanical behavior due to the reduction of scale. Size effects have been considerably studied recently for materials with various crystallographic structures. Under tensile conditions, thin specimen exhibit softer mechanical properties when the number of grains across thickness is lower than a critical number and this modification appears above a critical strain level. In this work, stamping tests were performed on five hundred micrometers in thickness sheets of hexagonal closed-packed cobalt. The results are compared with those obtained for face centered cubic copper and nickel. The influence of thickness over grain size ratio was studied for several proportional loadings linked to forming processes. Complex loadings were applied with 20 mm hemispherical punch and strain paths were checked with a 3D video extensometer. Hill criterion was systematically used to take into account the anisotropy of the samples. Our results revealed that the critical strain level for which the size effects appears is strongly sensitive to the stress triaxiality which, in turn, is closely dependent to the loading path.

Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images

Beyond bone mineral density (BMD), bone quality designates the mechanical integrity of bone tissue. In vivo images based on X-ray attenuation, such as CT reconstructions, provide size, shape, and local BMD distribution and may be exploited as input for finite element analysis (FEA) to assess bone fragility. Further key input parameters of FEA are the material properties of bone tissue. This review discusses the main determinants of bone mechanical properties and emphasizes the added value, as well as the important assumptions underlying finite element analysis. Bone tissue is a sophisticated, multiscale composite material that undergoes remodeling but exhibits a rather narrow band of tissue mineralization. Mechanically, bone tissue behaves elastically under physiologic loads and yields by cracking beyond critical strain levels. Through adequate cell-orchestrated modeling, trabecular bone tunes its mechanical properties by volume fraction and fabric. With proper calibration, these mechanical properties may be incorporated in quantitative CT-based finite element analysis that has been validated extensively with ex vivo experiments and has been applied increasingly in clinical trials to assess treatment efficacy against osteoporosis.

Numerical and experimental studies on deformation behavior of 5083 aluminum alloy strips in equal channel angular rolling

Improvement of mechanical properties of metal strips can be achieved by producing ultra-fine grained microstructure. The equal channel angular rolling process is one of the effective severe plastic deformation techniques which can lead to proper ultra-fine grained structures. In this research, the influence of process parameters such as pre–equal channel angular rolling annealing temperature, number of equal channel angular rolling passes, routes and post–equal channel angular rolling annealing on deformation behavior of 5083 Al alloy is investigated by experimental studies and numerical simulations. Metallurgical investigations revealed that grain refinement and increased dislocation density are two effective parameters on the mechanical strength improvement. The investigation of mechanical properties demonstrated that increasing number of equal channel angular rolling passes leads to a considerable increase in yield stress, ultimate tensile strength and hardness. In contrast, elongation was dramatically reduced. Also, improvement of mechanical properties reaches saturation at a critical strain level, depending on the microstructure evolution. In addition, investigation of effects of post–equal channel angular rolling annealing on the specimens annealed at 415 °C indicated that elongation and toughness increase, accompanying with a low decrease in yield and tensile strengths and hardness. In this study, the equal channel angular rolling process was numerically simulated using ABAQUS software in two different routes for three passes. It is shown that upper roller force is increased by increasing the number of equal channel angular rolling passes, but the rate of this increase is reduced at higher passes.