Anisotropic continuum damage model for prediction of failure in flax/polypropylene fabric composites

An anisotropic continuum damage modeling approach was applied to model failure of a composite of unidirectional flax in a polypropylene matrix under quasi‐static tensile loading. Tensile, compressive and shear stiffness, and strength values of the composite were characterized according to ASTM standards, and the damage was quantified by optical microscopy. Based on the experimental strength and damage values, an anisotropic strain‐dependent material damage model was developed and implemented in the finite element program ABAQUS. This was combined with geometric models of the fabric composites incorporating the yarn geometry. Good agreement was observed between the experimental and numerical stress–strain curves, and the failure strength prediction by the model was within 3.1% of the experimental value. This study shows that combining a geometric model closely incorporating the actual geometry of a fabric composite with an experimentally determined material degradation model can yield good predictions of the mechanical behaviour of the composite. POLYM. COMPOS., 37:2588–2597, 2016. © 2015 Society of Plastics Engineers     

Damage modeling of oxide/oxide ceramic matrix composites under cyclic loading conditions

Ceramic matrix composites exhibit optimal high temperature property and complex nonlinear behaviors including irreversible deformations and stiffness degradation under different mechanical loading conditions. In the present work, the damage evolution of the material under multi-axial loads considering effects of loading-unloading cyclic was studied and a novel continuum damage constitutive model was proposed. The material degradation was decomposed into monotonic damages and cyclic damages. The anisotropic hardening behavior of the material was considered by taking orientation dependence into account. Compared to the experimental results, the constitutive model could accurately predict the stress-strain response and stiffness degradations of the oxide/oxide ceramic matrix composites for monotonic loading and cyclic loading.     

Poroplastic damage model for claystones

The aim of this work is to propose a poroplastic damage model for claystones. Based on experimental results, this model reproduces the effects induced by degradations of the porous matrix after a mechanical loading.First, an anisotropic poroplastic damage model is formulated in order to describe the material degradations. According with the experimental observations, a plastic yield function based on the Drücker–Prager criterion is used, while considering an isotropic plastic hardening. Furthermore, as for most rocks, the plastic flow is non-associated.In order to take into account the induced anisotropy, the damage is represented by a second-order tensor. The interest of the damage elastic constitutive law is the effective stress, which allows the coupling with plasticity. The triaxial drained tests were then simulated under different confining pressures. The comparison with the experimental results is very satisfactory.Finally, the plastic damage model is reformulated in order to take into account the damage influences on the hydromechanical behaviour of the rock. Using the results of micromechanics analysis and assuming initial isotropy and microhomogeneity of the material, we obtained Biot coefficient tensor according to the damage variable. In order to quantify the influence of the damage on the poromechanics coefficient value, numerical simulations were carried out.     

Progressive damage modeling of adhesively bonded lap joints

A continuum damage model for simulating damage propagation of bonded joints is presented, introducing a linear softening damage process for the adhesive agent. Material models simulating anisotropic non-linear elastic behavior and distributed damage accumulation were used for the composite adherends as well. The proposed modeling procedure was applied to a series of lap joints accounting for adhesion either by means of secondary bonding or co-bonding. Stress analysis was performed using plane strain elements of a commercial finite element code allowing implementation of user defined constitutive equations. Numerical results for the different overlap lengths under investigation were in good agreement with experimental data in terms of joint strength and overall structural behavior.     

Damage and failure mechanism of sapphire under ballistic loading based on a modified bond-based peridynamic model

To investigate the dynamic mechanical behaviors of c-plane and a-plane sapphire, a novel anisotropic constitutive model and fracture criterion are constructed on the basis of bond-based peridynamics (BB-PD) theory. And the concept of strain is introduced in the framework of BB-PD. After that, the simulations of a- and c-planes of sapphire under spherical and cylindrical impact are conducted. In addition to capturing the distribution of strain and damage, the histories of various fracture types such as the primary fracture front and cracks are monitored for quantitative analysis. The numerical predictions are shown to agree well with previous experimental results, and further reveal the damage and failure mechanisms of sapphire. The different forms of contact between the projectile and the target strongly influence the stress waves generated and energy transferred ultimately affecting the damage development process. The crystal orientation dominates the appearance of anisotropic crack modes. Crack bending and deflection, as well as spalling-like fracture, are associated with wave reflection and intersection. Moreover, an in-depth examination of the observed wave splitting phenomenon is performed.     

A constitutive model for non‐linear behavior of SMC accounting for linear viscoelasticity and micro‐damage

An approach for modeling sheet molding compound (SMC) composites as viscoelastic damageable material is presented. Continuum damage mechanics theory by Chow and Wang (Int. J. Fract., 33, 3 (1987)) was used in combination with linear viscoelasticity. The model was applied to a modern SMC composite material containing both hollow glass spheres for low density and toughening additive for improved impact resistance. Tensile tests and uniaxial creep test were employed to build the constitutive model. Validation was done by comparing test data with simulations of uniaxial creep on material with different degrees of damage. The model has good accuracy at moderate damage levels under controlled time‐dependent crack propagation. Tensile testing at two different fixed strain rates was simulated using quasi‐elastic method to calculate relaxation modulus. The model predicts the stress‐strain curve with good accuracy until the region is close to failure, where new mechanisms not accounted for are taking place. Finally, a simulation of a cyclic tensile test with increasing maximum strain per cycle was performed, and since both damage and viscoelasticity are included in the model, the slope change, accumulation of residual strain, and hysteresis in the stress‐strain, loading‐unloading curve are predicted. POLYM. COMPOS., 26:84–97, 2005. © 2004 Society of Plastics Engineers     

Constitutive modeling of injection-molded short-fiber composites: Characterization and model application

A previously developed constitutive model for short-fiber reinforced thermoplastics is applied to an injection-molded component with a complex geometry and microstructure. This macro-scale continuum-based model is able to capture the anisotropic viscoelastic-viscoplastic response of the material. In injection-molded short-fiber composites, the anisotropic mechanical properties depend strongly on the fiber orientation distribution, which generally displays a marked variation throughout the product. This makes the material characterization and model application challenging. In this article, two characterization and model application strategies are proposed. These techniques, together with the developed constitutive model provide a strong tool for reliable prediction of the mechanical response of an injection molded product, where inputs to the finite element analysis are obtained directly from a numerical simulation of the injection molding process. In this article, from the output provided by an injection molding process simulation software such as Moldflow, the distribution of anisotropic elastic and plastic properties throughout the component is found and the data is imported to the finite element mesh. Mechanical tests are performed on a validation product and results are compared with model predictions from finite element simulations. Through this comparison, the performance of the constitutive model and also proposed procedures for characterization and model application are investigated.     

A micromechanical damage model for oxide/oxide ceramic matrix composites with hierarchical porosity under thermomechanical loading

This work presents a micromechanical damage model to describe the microstructural damage behaviors of ceramic matrix composites with hierarchical porosity during thermomechanical loading. The microstructure evolution may cause the nonlinear constitutive behavior, and a hierarchical porosity-based elasto-plastic constitutive model was developed. Damage mechanisms of matrix-crack, hierarchical pore nucleation and fiber-breaking are incorporated into the formulation of the damage model to describe various micromechanical damage modes of ceramic matrix composites accurately. Two damage variables are proposed for the damage evolution of matrix and fiber bundles. The main damage mechanisms in the matrix are matrix-cracking, and fibers breaking in the fiber bundles. The performance of the proposed damage model is verified by comparing with the existing experimental data. The proposed damage model outperforms the existing counterparts by capturing the microstructural damage mechanism and integrated into the damage model, and the contribution of different damage mechanisms can be quantified. The present work will provide a robust tool for describing the damage behaviors of matrix and fiber bundles in the ceramic matrix composites under thermomechanical loading, as well as allow a more accurate characterization of microstructural damage for a large extent of ceramic matrix composites.     

A constitutive model for the nonlinear viscoplastic behavior of thermoplastic olefin

A tangent constitutive model was developed in this article to address the nonlinear viscoplastic behavior of compound grade thermoplastic olefin (TPO). The TPO was commonly blends of polypropylene matrix, rubber, and inorganic filler. The constitutive model for TPO was obtained from the combination of the mechanical behavior of the matrix and fillers. In a multiphase material, the rate‐dependent behavior of polypropylene matrix was presented by a physically based constitutive model for large strain deformation, while the deformation behavior of rubber and talc were captured by Hooke's law. The average strain of each phase, as well as the strain of the voids caused by cavitation of rubber and debonding of talc, was determined by the Mori‐Tanaka method, in conjunction with a tangent modulus approach. To test the applicability of the developed model, it was applied to calculate the rate dependent stress‐strain relations of TPO. The model was predictive of the initial rate‐dependent stiffness, yield, and strain hardening response in large strain deformation. The constitutive model was incorporated into a finite element code to predict the large strain deformation behavior of TPO. The initiation of necking and neck propagation were obtained and confirmed by experimental observation. POLYM COMPOS., 2010. © 2009 Society of Plastics Engineers     

岩石爆破中塑性压剪损伤的数值模拟

为计算爆破导致的塑性压剪损伤，基于岩石微元强度分布的随机性，采用连续介质力学与损伤力学理论，建立一种岩石损伤软化统计本构模型，并将此模型合理地嵌入到大型有限元软件LS-DYNA中，对无限岩体中的球形和柱形药包爆破压剪损伤问题进行了数值模拟，获得了不同围压下的应力-应变关系数据和不同时刻损伤分布的资料。该模型本构参数少，能够较好地反映出介质的损伤与软化等特征。     

Studies on rate dependent damage evolution in polymer blends in high strain rates

Abstract

The dynamic damage evolution and the damage modified constitutive response for polypropylene-polyamide polymer blends with different compatibilisers are experimentally investigated by a new technique, namely by combining the split Hopkinson pressure bar technique with the back propagation neural network. The results reveal that the damage evolution including the threshold condition for the beginning of damage evolution, are dependent on both strain and strain rate. Thus for viscoelastic materials, particularly for polymer blends or composites, mechanical behaviour with damage evolution should be evaluated in a wide range of strain rates.     

Experimental and simulative investigation into the mechanical behaviors of polypropylene with craze damage in different weakening processes

This article focused on the experimental and simulative investigation into the mechanical behaviors of polypropylene (PP) at different strain rates. With the aim to describe the crazing yielding of PP, an elastoviscoplastic constitutive model with damage behavior was established and embedded into the finite element codes in the Abaqus platform. The simulation results are in good accordance with the experimental ones. Moreover, the influence of different weakening processes on the material properties was explored. In comparison to the nonweakened specimen, the weakened specimen exhibited nonlinear yielding properties under lower stress. Noteworthily, the integral strength of the weakened specimen proves to be linearly dependent on the cross‐section area of the weakening zone. Eventually, the damage model of simplified dashboard was utilized to study the damage law of the dashboard with V‐shaped weakening line. Results show the crack initially emerged at the weakening line and then rapidly expanded till the ends of the damage, which satisfied the damage requirements of practical dashboard. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41475.     

Constitutive model and failure criterion for orthotropic ceramic matrix composites under macroscopic plane stress

To predict the nonlinear stress-strain behavior and the rupture strength of orthotropic ceramic matrix composites (CMCs) under macroscopic plane stress, a concise damage-based mechanical theory including a new constitutive model and two kinds of failure criteria was developed in the framework of continuum damage mechanics (CDM). The damage constitutive model was established using strain partitioning and damage decoupling methods. Meanwhile, the failure criteria were formulated in terms of damage energy release rate (DERR) in order to correlate the failure property of CMCs with damage driving forces, and the maximum DERR criterion and the interactive DERR criterion were suggested simultaneously. For the sake of model evaluation, the theory was applied to a typical CMC with damageable and nonlinear behavior, that is, 2D-C/SiC. The damage evolution law, strain response and rupture strength under incremental cyclic tension along both on-axis and off-axis directions were completely investigated. Comparison between theoretical predictions and experimental data illustrates that the newly developed mechanical theory is potential to give reasonable and accurate results of both stress-strain response and failure property for orthotropic CMCs.     

New constitutive model for anisotropic hyperelastic biased woven fibre reinforced composite

Abstract

This paper presents an improved constitutive model having application in finite element analysis of composites made of hyperelastic matrix with biased woven fabric reinforcement and is based on a pragmatic approach and the continuum mechanics theory. A generalised strain energy function is developed via a series of uniaxial tests in fibre warp and weft directions and via shear tests of representative samples of composite fabric. The proposed material characterisation approach is demonstrated on composites made of neoprene rubber matrix with nylon biased woven reinforcements having volume fraction composition 0·74 vol.-% neoprene and 0·26 vol.-% nylon. The material parameters in the anisotropic hyperelastic model are obtained by minimisation of least square residuals of uniaxial and pure shear energy densities against the respective strain invariants. Numerical simulations of uniaxial and bulge tests of the composites using the material model presented in this paper are shown to correspond well with results obtained from laboratory experiment.     

Strain rate influence on nonlinear response of polymer matrix composites

In this article, influence of strain rate on nonlinear response of unidirectional fiber‐reinforced composites is studied. The fibers are assumed to be periodic arrays in composite structures. By studying a representative volume element, a microscopic constitutive model for characterizing macro‐mechanical response of polymer matrix composites is developed. Viscoplastic material parameters of polymer matrix are acquired by axial tension and pure shear experiment, and the proposed method is validated by experimental data. The results showed that mechanical behavior of composites, which is affected by strain rate, can be ignored in the linear stage of loading. Furthermore, with the increase in strain rate, stiffness behavior of composites tends to be stiffer at the stage of nonlinear deformation. POLYM. COMPOS., 36:800–810, 2015. © 2014 Society of Plastics Engineers     

Modeling creep behavior in ceramic matrix composites

In this work, a three-dimensional viscoplasticity formulation with progressive damage is developed and used to investigate the complex time-dependent constituent load transfer and progressive damage behavior in ceramic matrix composites (CMCs) subjected to creep. The viscoplasticity formulation is based on Hill's orthotropic plastic potential, an associative flow rule, and the Norton-Bailey creep power law with Arrhenius temperature dependence. A fracture mechanics-informed isotropic matrix damage model is used to account for CMC brittle matrix damage initiation and propagation, in which two scalar damage variables capture the effects of matrix porosity as well as matrix property degradation due to matrix crack initiation and propagation. The Curtin progressive fiber damage model is utilized to simulate progressive fiber failure. The creep-damage formulation is subsequently implemented as a constitutive model in the generalized method of cells (GMC) micromechanics formulation to simulate time-dependent deformation and material damage under creep loading conditions. The developed framework is used to simulate creep of single fiber SiC/SiC microcomposites. Simulation results are in excellent agreement with experimental and numerical data available in the literature.     

Simulation of the residual stresses in the contour laser welding of thermoplastics

This article presents the influence of the process parameters in laser transmission welding for plastics on the residual stress in the welded part. The contour welding process is modeled by means of finite element (FE) simulation. In this process, the weld seam is only partially heated, i.e., only part of it melts. The calculations are performed using a material model that describes the time‐dependent temperature and stress development in a plate geometry, making allowance for the material's asymmetric compressive‐tensile behavior. Experimental data were measured under different load cases to present the time‐dependent material behavior, and then implemented in numerical terms by formulating the necessary constitutive equations. The calculations to simulate the influence of process parameters on the residual stress behavior were performed using a finite element model that was developed. The simulation covers the entire welding process, including the heating and cooling stages. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Characterisation of damage mechanisms in oxide ceramics indented at dynamic and quasi-static strain rates

Ceramic materials are known to display rate dependent behaviour under impact. Tests to establish the strain-rate dependent variations in damage mechanisms have been carried out on debased alumina, an alumina-zirconia composite, and 3Y-TZP. Materials were indented dynamically and quasi-statically using identical sharp hardened steel projectiles while recording the load profile. Characteristics typical of both sharp and blunt indentation types were observed using scanning electron microscopy and piezospectroscopic mapping. At dynamic strain rates both the depth of the indentation and the residual stress in the material were lower than for quasi-static tests. This was attributed to temperature-induced softening of the projectile. Unusual behaviour was observed in the 3Y-TZP samples due to the reversible transformation from tetragonal to monoclinic crystal structures during mechanical loading. These effects and the observed superior mechanical strength against impact suggest that zirconia or zirconia-composite materials may have advantages over debased alumina for application as ceramic armour materials.