Micromechanical analysis of damage in saturated quasi brittle materials

In this paper, we propose a micromechanical analysis of damage and related inelastic deformation in saturated porous quasi brittle materials. The materials are weakened by randomly distributed microcracks and saturated by interstitial fluid with drained and undrained conditions. The emphasis is put on the closed cracks under compression-dominated stresses. The material damage is related to the frictional sliding on crack surface and described by a local scalar variable. The effective properties of the materials are determined using a linear homogenization approach, based on the extension of Eshelby’s inclusion solution to penny shaped cracks. The inelastic behavior induced by microcracks is described in the framework of the irreversible thermodynamics. As an original contribution, the potential energy of the saturated materials weakened by closed frictional microcracks is determined and formulated as a sum of an elastic part and a plastic part, the latter entirely induced by frictional sliding of microcracks. The influence of fluid pressure is accounted for in the friction criterion through the concept of local effective stress at microcracks. We show that the Biot’s effective stress controls the evolution of total strain while the local Terzaghi’s effective stress controls the evolution of plastic strain. Further, the frictional sliding between crack lips generates volumetric dilatancy and reduction in fluid pressure. Applications of the proposed model to typical brittle rocks are presented with comparisons between numerical results and experimental data in both drained and undrained triaxial tests.     

Higher-order theory for periodic multiphase materials with inelastic phases

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress and inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model and with finite-element results for transverse loading.     

压剪复合冲击下氧化铝陶瓷的剪切响应实验研究

通过对92.93%氧化铝陶瓷进行倾斜板碰撞实验,研究了多晶陶瓷材料在压剪复合冲击下的非弹性变形响应和剪切波传播规律。压剪复合冲击实验由57 mm开槽气体炮驱动铜飞片对陶瓷靶板加载,通过试件内埋植的电磁速度计来测量内部质点速度历程。将纵向粒子速度从感应电动势曲线中分离后得到横向粒子速度历程,发现在压剪复合冲击下由于材料剪切刚度的降低而引起的剪切波衰减。冲击软回收试件的扫描电子显微镜（SEM）观察表明,冲击载荷低于屈服强度时,多晶氧化铝陶瓷中存在沿晶界、气孔的微裂纹成核与扩展,在高于屈服强度的冲击加载下进一步产生了穿晶微裂纹,微裂纹系统导致了材料在卸载后的显著的体积膨胀。     

Prediction of the softening and damage effects with permanent set in fibrous biological materials

Deformation induced softening is an inelastic phenomenon frequently accompanying mechanical response of soft biological tissues. Inelastic phenomena which occur in mechanical testing of biological tissues are very likely to be associated with alterations in the internal structure of these materials.In this study, a novel structural constitutive model is formulated to describe the inelastic effects in soft biological tissues such as Mullins type behavior, damage and permanent set as a result of residual strains after unloading. Anisotropic softening is considered by evolution of internal variables governing the anisotropic properties of the material. We consider two weight factors w_i (softening) and s_k (discontinuous damage) as internal variables characterizing the structural state of the material. Numerical simulations of several soft tissues are used to demonstrate the performance of the model in reproducing the inelastic behavior of soft biological tissues.     

A material force method for inelastic fracture mechanics

A material force method is proposed for evaluating the energy release rate and work rate of dissipation for fracture in inelastic materials. The inelastic material response is characterized by an internal variable model with an explicitly defined free energy density and dissipation potential. Expressions for the global material and dissipation forces are obtained from a global balance of energy-momentum that incorporates dissipation from inelastic material behavior. It is shown that in the special case of steady-state growth, the global dissipation force equals the work rate of dissipation, and the global material force and J-integral methods are equivalent. For implementation in finite element computations, an equivalent domain expression of the global material force is developed from the weak form of the energy-momentum balance. The method is applied to model problems of cohesive fracture in a remote K-field for viscoelasticity and elastoplasticity. The viscoelastic problem is used to compare various element discretizations in combination with different schemes for computing strain gradients. For the elastoplastic problem, the effects of cohesive and bulk properties on the plastic dissipation are examined using calculations of the global dissipation force.     

Cyclic plasticity modeling with the distribution of non-linear relaxations approach

Motivated by the distribution of non-linear relaxation (DNLR) approach, a phenomenological model is proposed in order to describe the cyclic plasticity behavior of metals under proportional and non-proportional loading paths with strain-controlled conditions. Such a model is based on the generalization of the Gibbs's relationship outside the equilibrium of uniform system and the use of the fluctuation theory to analyze the material dissipation due to its internal reorganization. The non-linear cyclic stress–strain behavior of metals notably under complex loading is of particular interest in this study. Since the hardening effects are described appropriately and implicitly by the model, thus, a host of inelastic behavior of metals under uniaxial and multiaxial cyclic loading paths are successfully predicted such as, Bauschinger, strain memory effects as well as additional hardening. After calibrating the model parameters for two metallic materials, the model has demonstrated obviously its ability to describe the cyclic elastic-inelastic behavior of the nickel base alloy Waspaloy and the stainless steel 316L. The model is then implemented in a commercial finite element code simulating the cyclic stress–strain response of a thin-walled tube specimen. The numerical responses are in good agreement with experimental results.     

PROGRESSIVE FRACTURE MODELING OF THE FAILURE WAVE IN IMPACTED GLASS

The failure wave has been observed propagating in glass under impact loading since 1991. It is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. A progressive fracture model was proposed to describe the failure wave formation and propagation in shocked glass considering its heterogeneous meso-structures. The original and nucleated microcracks will expand along the pores and other defects with concomitant dilation when shock loading is below the Hugoniot Elastic Limit. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from the collapse of the original pores. Numerical simulation of the free surface velocity was performed and found in good agreement with planar impact experiments on K9 glass at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.     

A crack-mechanics based model for damage and plasticity of brittle materials under dynamic loading

A rate-dependent model for damage and plastic deformation of brittle materials under dynamic loading is presented. The model improves upon a recently developed micromechanical damage model (Zuo et al., 2006) by incorporating plastic deformation of the material. The distribution of the microcracks in the material is assumed to remain isotropic, and the damage evolution is through the growth of the average crack size. Plasticity is considered through an additive decomposition of the total strain rate, and a rate-independent, von Mises model is used. The model was applied to simulate the response of a model material (SiC) under uniaxial strain loading. To further examine the behavior of the model, cyclic loading and large-strain compressive loading were considered. Numerical results of the model predictions are presented, and comparisons with those from a previous model are provided.     

A simple method for calculating interaction of numerous microcracks and its applications

The effects of microcrack interaction on the failure behavior of materials present one problem of considerable interest in micromechanics, which has been extensively argued but has not been resolved as yet. In the present paper, a simple and effective method is presented based on the concept of the effective field to analyze the interaction of microcracks of a large number or of a high density. To determine the stress intensity factors of a microcrack embedded in a solid containing numerous or even countless microcracks, the solid is divided into two regions. The interaction of microcracks in a circular or elliptical region around the considered microcrack is calculated directly by using Kachanov’s micromechanics method, while the influence of all other microcracks is reflected by modifying the stress applied in the far field. Both the cases of tensile and compressive loading are considered. This simplified scheme may yield an estimate for stress intensity factors of satisfactory accuracy, and therefore provide a potential tool for elucidating some phenomena of material failure associated with microcracking. As two of its various promising applications, the above scheme is employed to investigate the size effects of material strength due to stochastic distribution of interacting microcracks and to calculate the effective elastic moduli of elastic solids containing distributed microcracks. Some conventional micromechanics methods for estimating the effective moduli of microcracked materials are evaluated by comparing with the numerical results. Only two-dimensional problems have been considered here, though the three-dimensional extension of the present method is of greater interest.     

Stress-resultant plasticity theories for composite laminated plates

Constitutive laws are presented for the inelastic analysis of laminated composite plates. The implications of using an elastoplastic theory, applied in a stress-resultant formulation, are discussed and investigated. Two different stress-resultant plasticity theories are proposed, both of which overlook the matrix and fiber inelastic behavior and describe the inelastic response of the laminate as a function of overall laminate properties. Results from numerical experiments with the proposed models are compared with results obtained using a micromechanical elastoplastic composite constitutive model.     

Constitutive behavior of superplastic materials

Superplasticity is an intriguing inelastic process in solid materials with deformation upto several thousand percent. Forming sheet and bulk materials using superplastic forming has become an established manufacturing method in aerospace and lately in other industries. Developing the right constitutive behavior is important not only for modeling the process for manufacturing by engineering mechanicians but for choosing the right composition and processing for material scientists. Such an ideal constitutive equation has been eluding the analysts so far. This paper examines some of the fundamental misgivings about the origin of inelastic process in superplasticity compared to other well known deformation processes. Also an attempt is made to understand the basic characteristics of superplastic inelastic deformation at macroscopic, mesoscopic and atomic levels.     

修正的Bodner-Partom本构模型

对于含有微损伤的多孔介质,由于微裂纹和微孔洞的存在,从宏观角度看,非弹性体应变会随着外载荷的变化而发生改变,即非弹性体应变不应为零。本文修正了计及损伤效应的Bodner-Partom本构模型。并以修正的本构模型对LY-12硬铝材料受到电子束辐照时产生的热击波及材料的创伤破坏效应进行了理论计算,将计算值同实验结果比较表明,两者基本上是一致的。     

Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials

Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes occurring in the internal heterogeneous structure. These models tend to be intensive from the computational point of view as they adopt an “a priori” discretization anchored to the major material heterogeneities (e.g. grains in particulate materials and aggregate pieces in cementitious composites) and this hampers their use in the numerical simulations of large systems. In this work, this problem is addressed by formulating a general multiple scale computational framework based on classical asymptotic analysis and that (1) is applicable to any discrete model with rotational degrees of freedom; and (2) gives rise to an equivalent Cosserat continuum. The developed theory is applied to the upscaling of the Lattice Discrete Particle Model (LDPM), a recently formulated discrete model for concrete and other quasi-brittle materials, and the properties of the homogenized model are analyzed thoroughly in both the elastic and the inelastic regime. The analysis shows that the homogenized micropolar elastic properties are size-dependent, and they are functions of the RVE size and the size of the material heterogeneity. Furthermore, the analysis of the homogenized inelastic behavior highlights issues associated with the homogenization of fine-scale models featuring strain-softening and the related damage localization. Finally, nonlinear simulations of the RVE behavior subject to curvature components causing bending and torsional effects demonstrate, contrarily to typical Cosserat formulations, a significant coupling between the homogenized stress–strain and couple-curvature constitutive equations.     

Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method

This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.     

On the stored and dissipated energies in heterogeneous rate-independent materials

The present paper is a part of a work that aims at building a dissipative model of microcrack friction in quasi-brittle energetic materials. The latter is viewed as an assembly of elementary cells containing the most salient features of the microstructure heterogeneity. It is intended here to build an analytical model describing the mechanical and energetic response of such an elementary cell under confined tension. This is achieved by applying a previously published theory that allows for the determination of the amount of dissipated and stored energies in heterogeneous dissipative structures containing microcracks and other dissipative components.     

Large deformation of anisotropic austenitic stainless steel sheets at room temperature: Multi-axial experiments and phenomenological modeling

A newly developed multi-axial testing technique for sheet materials is employed to investigate the inelastic response of a temper-rolled stainless steel 301LN under isothermal quasi-static loading conditions at room temperature. The experimental technique consists of a flat sheet specimen, which is subject to combinations of shear and normal loading using a custom-made dual-actuator system. The large deformation behavior under monotonic loading is determined along more than 20 distinct radial paths in the stress space. The experimental results indicate that Hill's quadratic yield function along with an associated flow rule provides a good approximation of the initial yield behavior of this anisotropic two-phase FCC/BCC sheet material. Based on the experimental data for radial monotonic loading, it is concluded that conventional isotropic-kinematic hardening models cannot successfully describe the strain hardening of this austenitic steel. Instead, a non-associated anisotropic hardening model is proposed that relates the increase in yield strength to an isothermal martensitic transformation kinetics law. The comparison of the model predictions with the experimental results shows very good agreement for all biaxial and uniaxial experiments.     

An effective temperature theory for the nonequilibrium behavior of amorphous polymers

Amorphous polymers lack an organized microstructure, yet they exhibit structural evolution, where physical properties change with time, temperature, and inelastic deformation. To describe the influence of structural evolution on the mechanical behavior of amorphous polymers, we developed a thermomechanical theory that introduces the effective temperature as a thermodynamic state variable representing the nonequilibrium configurational structure. The theory couples the evolution of the effective temperature and internal state variables to describe the temperature-dependent and rate-dependent inelastic response through the glass transition. We applied the theory to model the effect of temperature, strain rate, aging time, and plastic pre-deformation on the uniaxial compression response and enthalpy change with temperature of an acrylate network. The results showed excellent agreement with experiments and demonstrate the ability of the effective temperature theory to explain the complex thermomechanical behavior of amorphous polymers.     

Effects of matrix inelasticity on the overall hysteretic behavior of TiNi-SMA fiber composites

The effects of the inelastic deformation of the matrix on the overall hysteretic behavior of a unidirectional titanium–nickel shape-memory alloy (TiNi-SMA) fiber composite and on the local pseudoelastic response of the embedded SMA fibers are studied under the isothermal loading and unloading condition. The multiaxial phase transformation of the SMA fibers is predicted using the phenomenological constitutive equations which can describe the two-step deformation due to the rhombohedral and martensitic transformations, and the inelastic behavior of the matrix material using the standard nonlinear viscoplastic model. The average behavior of the SMA composite is evaluated with the micromechanical method of cells. It is observed that the inelastic deformation of the matrix due to prior tension results in a compressive stress in the matrix after unloading of the SMA composite and this residual stress impedes the complete recovery of the pseudoelastic strain of the SMA fibers. This explains that a closed hysteresis behavior of the SMA composite is no longer observed in contrast with the case that an elastic behavior of matrix is assumed. The predicted local stress–strain behavior indicates that the cyclic response of matrix is crucial to the design of the hysteretic performance of the SMA composite under the repeated loading conditions.     

Three-dimensional constitutive model for shape memory alloys based on microplane model

A new model for the behavior of polycrystalline shape memory alloys (SMA), based on a statically constrained microplane theory, is proposed. The new model can predict three-dimensional response by superposing the effects of inelastic deformations computed on several planes of different orientation, thus reproducing closely the actual physical behavior of the material. Due to the structure of the microplane algorithm, only a one-dimensional constitutive law is necessary on each plane. In this paper, a simple constitutive law and a robust kinetic expression are used as the local constitutive law on the microplane level. The results for SMA response on the macroscale are promising: simple one-dimensional response is easily reproduced, as are more complex features such as stress-strain subloops and tension-compression asymmetry. A key feature of the new model is its ability to accurately represent the deviation from normality exhibited by SMAs under nonproportional loading paths.