Simulation of failure under cyclic plastic loading by damage models

The purpose of this work is to simulate the evolution of ductile damage and failure involved by plastic strain reversals using damage models based on either continuum damage mechanics (CDM) or porosity evolution. A low alloy steel for pressure vessels (20MnMoNi55) was chosen as reference material. The work includes both experimental and simulation phases. The experimental campaign involves different kinds of specimens and testing conditions. First, monotonic tensile tests have been performed in order to evaluate tensile and ductile damage behaviour. Then, the cyclic yielding behaviour has been characterized performing cyclic plasticity tests on cylindrical bars. Finally, cyclic loading tests in the plastic regime have been made on different round notched bars (RNBs) to study the evolution of plastic deformation and damage under multiaxial stress conditions. The predictions of the different models were compared in terms of both, the specimens macroscopic response and local damage. Special emphasis was laid on predictions of the number of cycles prior to final failure and the crack initiation loci.     

Homogenization of long fiber reinforced composites including fiber bending effects

This paper presents a homogenization method, which accounts for intrinsic size effects related to the fiber diameter in long fiber reinforced composite materials with two independent constitutive models for the matrix and fiber materials. A new choice of internal kinematic variables allows to maintain the kinematics of the two material phases independent from the assumed constitutive models, so that stress–deformation relationships, can be expressed in the framework of hyper-elasticity and hyper-elastoplasticity for the fiber and the matrix materials respectively. The bending stiffness of the reinforcing fibers is captured by higher order strain terms, resulting in an accurate representation of the micro-mechanical behavior of the composite. Numerical examples show that the accuracy of the proposed model is very close to a non-homogenized finite-element model with an explicit discretization of the matrix and the fibers.     

Tensile failure of micro-concrete: from mechanical tests to FE meso-model with the help of X-ray tomography

In this work, concrete is studied at meso-scale (aggregates, macro-pores and mortar matrix), where the local failure mechanisms are known to drive the macroscopic behaviour of the material. In order to highlight the impact of the mechanical and morphological properties of each phase (along with their interfaces), micro-concrete specimens are prepared with rather small dimensions compared to the size of the heterogeneities. X-ray tomography is used to reliably obtain the morphology of the heterogeneous meso-structure, which is then given as an input to a 3D FE meso-model with enhanced discontinuities. A uniaxial tensile numerical simulation is performed as a first application. To validate the numerical model, a uniaxial tensile test of the same micro-concrete specimen is performed inside the X-ray scanner and the in-situ evolution of the micro-structure is followed. Thus, both a direct validation of the model and a valuable insight of the 3D fracture mechanisms while the load progresses are obtained. After identification of the numerical parameters, comparison of experimental and numerical results reveals the capability of the meso-model to reproduce the actual material response (in terms of macroscopic strength, Young’s modulus and fracture patterns), with the explicit representation of the meso-scale heterogeneities being its key feature. To further challenge the meso-model, a new morphology coming from an X-ray scan of another characteristic micro-concrete specimen is introduced and its macroscopic behaviour is computed without a priori numerical identification. Starting from an X-ray scan in meso-scale, it is shown that the 3D meso-model is capable to predict the macroscopic behaviour and the failure patterns of the material.

     

The effect of microstructural representation on simulations of microplastic ratcheting

This paper assesses the sensitivity of cyclic plasticity to microstructure morphology by examining and comparing the microplastic ratcheting behavior of different idealized microstructures (square, hexagonal, tessellated, and digitized from experimental data). This analysis demonstrates the sensitivity of computational accuracy to the various approximations in microstructural representation. The methodology used to perform this study relies on a coupling between microstructural characterization, mechanical testing and numerical simulations to investigate the influence of the microstructure on the purely tensile uniaxial microplastic ratcheting behavior of pure nickel polycrystals. The morphology and deformation behavior of polycrystals were characterized using electron back-scatter diffraction (EBSD), while a finite element model (FEM) of crystal plasticity was used in a computational framework. The predicted cyclic behavior is compared to experimental results both at the macroscopic and microstructural scales. The stress–strain response is less sensitive to the details of the microstructural representation than might be expected with all representations displaying similar macroscopic constitutive response. However, the details of the plastic strain distribution at the microstructural scale and the related estimations of damage mechanics vary substantially from one microstructural representation to another.     

On the evolution of lattice deformation in austenitic stainless steels—The role of work hardening at finite strains

In this work, a three dimensional crystal plasticity-based finite element model is presented to examine the micromechanical behaviour of austenitic stainless steels. The model accounts for realistic polycrystal micromorphology, the kinematics of crystallographic slip, lattice rotation, slip interaction (latent hardening) and geometric distortion at finite deformation. We utilise the model to predict the microscopic lattice strain evolution of austenitic stainless steels during uniaxial tension at ambient temperature with validation through in situ neutron diffraction measurements. Overall, the predicted lattice strains are in very good agreement with those measured in both longitudinal and transverse directions (parallel and perpendicular to the tensile loading axis, respectively). The information provided by the model suggests that the observed nonlinear response in the transverse {200} grain family is associated with a competitive bimodal evolution of strain during inelastic deformation. The results associated with latent hardening effects at the microscale also indicate that in situ neutron diffraction measurements in conjunction with macroscopic uniaxial tensile data may be used to calibrate crystal plasticity models for the prediction of the inelastic material deformation response.     

微结构对金属基复合材料宏观弹塑性性能的影响

采用广义自洽有限元迭代平均化方法分析ＳｉＣ晶须增强铝基复合材料的弹塑性拉伸行为，研究纤维长径与体分比的变化对复合材料宏观弹塑性变形的影响。通过细观应力场的分析，讨论基体内塑性区的发展与复合材料宏观弹塑性变形过程之间的联系，指出纤维端头处基体塑性区的发展将对复合材料拉伸弹塑性行为有着显著影响。最后，还讨论了以名义屈服应力σ０．２来表征金属基复合材料的弹塑性特征的不足之处。     

EFFECTS OF MICROSTRUCTURE ON THE MACROSCOPIC ELASTO-PLASTIC PROPERTIES OF METAL MATRIX COMPOSITES

The generalized self-consistent finite-element iterative averaging method was adopted toanalyze the elasto-plastic tensile properties of SiC whiskers reinforced aluminum matrix composites.The effects of varying fiber's aspect ratio and volume fraction on the macroscopic elasto-plastic defor-mation of the composites were studied.By the analysis of microscopic stress fields,the relation be-tween the propagation of the elasto-plastic region in the matrix and the macroscopic elasto-plastic de-formation of composites was discussed.It was found that the propagation of the plastic region in thematrix between the fiber's ends would affect prominently the elasto-plastic tensile behaviour of thecomposites.It was shown that the characterization of the stress-strain response in terms of the 0.2%offset yield strength is incomplete.     

Cyclic behaviour of short glass fibre reinforced polyamide: Experimental study and constitutive equations

Polymer matrix composites are widely used in the automotive industry and undergo fatigue loadings. The investigation of the nonlinear cyclic behaviour of such materials is a required preliminary work for a confident fatigue design, but has not involved many publications in the literature. This paper presents an extensive experimental study conducted on a polyamide 66 reinforced with 35 wt% of short glass fibres (PA66 GF35), at room temperature. The material was tested in two conditions: dry-as-moulded (DAM) and at the equilibrium with air containing 50% of relative humidity (RH50).An exhaustive experimental campaign in tensile mode has been carried out, including various strain or stress rates, complex mechanical histories and local thermo-mechanical recordings. Such an extended database allowed us to highlight several complex physical phenomena: viscoelastic effects at different time scales, irrecoverable mechanisms, non-linear kinematic hardening, non-linear viscous flow rule, cyclic softening.Taking into account this advanced analysis, a constitutive model describing the cyclic behaviour is proposed. As the experimental database only includes uniaxial tensile tests, the general 3D anisotropic frame is reduced to an uniaxial model valid for a specific orientation distribution. The robust identification process is based on tests which enable the uncoupling between the underlined mechanical features. This strategy leads to a model which accurately predicts the cyclic behaviour of conditioned as well as dry materials under complex tensile loadings.     

Pore Network Modelling of Electrical Resistivity and Capillary Pressure Characteristics

In order to model petrophysical properties of hydrocarbon reservoir rocks, the underlying physics occurring in realistic rock pore structures must be captured. Experimental evidence showing variations of wetting occurring within a pore, and existence of the so-called 'non-Archie' behaviour, has led to numerical models using pore shapes with crevices (for example, square, elliptic, star-like shapes, etc.). This paper presents theoretical derivations and simulation results of a new pore space network model for the prediction of petrophysical properties of reservoir rocks. The effects of key pore geometrical factors such as pore shape, pore size distribution and pore co-ordination number (pore connectivity) have been incorporated into the theoretical model. In particular, the model is used to investigate the effects of wettability and saturation history on electrical resistivity and capillary pressure characteristics. The petrophysical characteristics were simulated for reservoir rock samples. The use of the more realistic grain boundary pore (GBP) shape allows simulation of the generic behaviour of sandstone rocks, with various wetting scenarios. The predictions are in close agreement with electrical resistivity and capillary pressure characteristics observed in experiments.     

Experimental investigation of cyclic and time-dependent deformation of titanium alloy at elevated temperature

A novel cyclic deformation test program was undertaken to characterize macroscopic time dependent deformation of a titanium alloy for use in viscoplastic model development. All tests were conducted at a high homologous temperature, 650 °C, where there are large time dependent and loading rate dependent effects. Uninterrupted constant amplitude tests having zero mean stress or a tensile mean stress were conducted using three different control modes: strain amplitude and strain rate, stress amplitude and stress rate, and a hybrid stress amplitude and strain rate. Strain ratcheting occurred for all cyclic tests having a tensile mean stress and no plastic shakedown was observed. The shape of the strain ratcheting curve as a function of time is analogous to a creep curve having primary, steady state and tertiary regions, but the magnitude of the ratchet strains are higher than creep strains would be for a constant stress equal to the mean stress. Strain cycles interrupted with up to eight 2-h stress relaxation periods around the hysteresis loop, including hold times in each quadrant of the stress–strain diagram, were also conducted. Stress relaxation was path-dependent and in some cases the stress relaxed to zero. The cyclic behavior of these interrupted tests was similar even though each cycle was very complex. These results support constitutive model development by providing exploratory, characterization and validation data.     

Viscoelasticity of brain corpus callosum in biaxial tension

Computational models of the brain rely on accurate constitutive relationships to model the viscoelastic behavior of brain tissue. Current viscoelastic models have been derived from experiments conducted in a single direction at a time and therefore lack information on the effects of multiaxial loading. It is also unclear if the time-dependent behavior of brain tissue is dependent on either strain magnitude or the direction of loading when subjected to tensile stresses. Therefore, biaxial stress relaxation and cyclic experiments were conducted on corpus callosum tissue isolated from fresh ovine brains. Results demonstrated the relaxation behavior to be independent of strain magnitude, and a quasi-linear viscoelastic (QLV) model was able to accurately fit the experimental data. Also, an isotropic reduced relaxation tensor was sufficient to model the stress-relaxation in both the axonal and transverse directions. The QLV model was fitted to the averaged stress relaxation tests at five strain magnitudes while using the measured strain history from the experiments. The resulting model was able to accurately predict the stresses from cyclic tests at two strain magnitudes. In addition to deriving a constitutive model from the averaged experimental data, each specimen was fitted separately and the resulting distributions of the model parameters were reported and used in a probabilistic analysis to determine the probability distribution of model predictions and the sensitivity of the model to the variance of the parameters. These results can be used to improve the viscoelastic constitutive models used in computational studies of the brain.     

金属基复合材料和强度与损伤分析

用观察计算力学的方法分析了金属基复合材料（ＭＭＣ）多重损伤与强度的关系,采用唯象的内聚力模型模拟纤维／基体界面的脱粘和采用Ｇ－Ｔ模型描述韧性基体的损伤。并用上述模型分析了长纤维增强ＭＭＣ在横向荷载作用下损伤演化的规律,讨论了不同界面性质与材料强度及损伤、破坏模式之间的关系。     

A review of some plasticity and viscoplasticity constitutive theories

The purpose of the present review article is twofold:

•

recall elementary notions as well as the main ingredients and assumptions of developing macroscopic inelastic constitutive equations, mainly for metals and low strain cyclic conditions. The explicit models considered have been essentially developed by the author and co-workers, along the past 30 years;     

Characterization of macroscopic tensile strength of polycrystalline metals with two-scale finite element analysis

The objective of this contribution is to develop an elastic-plastic-damage constitutive model for crystal grain and to incorporate it with two-scale finite element analyses based on mathematical homogenization method, in order to characterize the macroscopic tensile strength of polycrystalline metals. More specifically, the constitutive model for single crystal is obtained by combining hyperelasticity, a rate-independent single crystal plasticity and a continuum damage model. The evolution equations, stress update algorithm and consistent tangent are derived within the framework of standard elastoplasticity at finite strain. By employing two-scale finite element analysis, the ductile behaviour of polycrystalline metals and corresponding tensile strength are evaluated. The importance of finite element formulation is examined by comparing performance of several finite elements and their convergence behaviour is assessed with mesh refinement. Finally, the grain size effect on yield and tensile strength is analysed in order to illustrate the versatility of the proposed two-scale model.     

Computational mechanics modelling of cell-substrate contact during cyclic substrate deformation

Experimental testing carried out on various adherent cell types cultured on deformable substrates reveals specific patterns of cell reorientation in response to cyclic stretching of the substrate. In Wang et al. (2001. Specificity of endothelial cell reorientation in response to cyclic mechanical stretching. J. Biomech. 34, 1563), a number of substrate deformation modes were considered: in cases where lateral deformation of the substrate was prohibited (uniaxial case) cells were found to elongate perpendicular to the stretch direction, whereas in cases where the substrate was laterally unrestrained (biaxial case) cells were found to elongate at an angle to the stretch direction. The alignment directions in both cases corresponded to directions of minimum substrate strain. However, the mechanisms underlying such behaviour are not apparent from such in-vitro testing and consequently are not well understood. In this study finite element models are developed in order to investigate the role of cell viscoelasticity in cell debonding and cell realignment under conditions of cyclic substrate stretching using cohesive zone formulations to simulate cell-substrate interfacial behaviour. The characteristic length scale used in such models is based on the length of the receptor-ligand bonds at the cell-substrate interface. Two-dimensional simulations reveal that permanent debonding at the cell-substrate interface occurs due to the accumulation of strain concentrations in the cell. Inclusion of a nucleus in two-dimensional models is shown to have little effect on debonding while discrete cell-substrate contact at focal adhesion sites results in a completion of debonding in fewer cycles. Three-dimensional cohesive zone models are developed in order to compute changes in cell-substrate contact under the aforementioned uniaxial and biaxial modes of substrate deformation. Results reveal that, due to the accumulation of tensile and compressive strains in the cell under cyclic deformation, definite patterns of cell-substrate contact area evolution are computed. With continued cycling, equilibrium contact area profiles with definite orientations are established. These orientations are found to be coincidental with the preferential cell orientation directions seen in the experiments. As no changes in cell morphology are predicted by the models it is concluded that permanent breaking of cell-substrate bonds constitutes the first stage in the process of cell alignment under such mechanical loading.     

含热冲击预损伤的陶瓷基复合材料损伤本构模型

陶瓷基复合材料结构在服役过程中不可避免地经受热冲击(较高的热应力梯度)而产生热机械损伤, 因此, 建立含循环热冲击预损伤材料的损伤本构模型, 以描述材料在热机械载荷作用下的力学行为, 对材料结构损伤容限设计与结构完整性评估非常重要. 本文首先对经历了循环热冲击的材料进行单调拉伸损伤实验, 发现对于含循环热冲击预损伤的材料, 其弹性模量的下降与所施加的应变直接相关. 然后在连续介质损伤力学的框架下, 基于平面应力假设, 建立了含循环热冲击预损伤材料的损伤演化模型, 该模型所涉及的参数可通过一个偏轴(45$^\circ$)以及两个正轴(平行于两个主方向)的单调拉伸试验获得. 最后, 采用经典塑性理论对由基体损伤引起的非弹性应变进行了描述. 本文所提出的应变损伤宏观模型可以描述陶瓷基复合材料在热机械载荷作用下的损伤演化, 同时弥补了含预损伤的陶瓷基复合材料在机械载荷下损伤本构模型在理论及实验研究方面的不足.      

Cyclic stress-strain behaviour of alloy AA6060 T4, part II: Biaxial experiments and modelling

Laboratory tests have been conducted to investigate the inelastic behaviour of aluminium alloy AA6060 T4 subjected to non-proportional cyclic loading. The results of four tests with variable strain path shapes and strain amplitudes are reported in this paper. The tests were carried out by applying combined axial force and torque to thin-walled tubular specimens, using effective strain amplitudes in the range 0.4–0.8%. Major emphasis has been put on the two important material properties: plastic anisotropy and influence of strain range and strain path shapes on cyclic hardening. A constitutive model for cyclic plasticity is used to predict the stress response of the alloy for the non-proportional strain paths applied in the experiments. The model adopts a quadratic yield function and multi-component non-linear isotropic and kinematic hardening rules to describe plastic anisotropy, the shape of the hysteresis loops and the evolution of cyclic hardening. Good agreement is obtained between the physical and correlated stress response of the alloy.