The effects of plastic deformation on stress wave propagation in multi-layer materials

The behavior of a multi-layer material at high strain rate and the effect of plastic deformation on stress wave propagation were investigated by a combination of experimental and numerical techniques. Plastic deformation effects were studied in multi-layer materials consisting of ceramic, copper and aluminum subjected to large strains under high strain rate loading. First, stress wave propagation behavior for the monolithic metals was studied, and then extended to multilayer combinations of these metals with each other and with a ceramic layer. The axial stress distributions were found to be non-uniform in the elastic deformation range of the specimen. The degree of non-uniformity was much more pronounced in the multi-layer samples consisting of different materials. The presence of a ceramic layer increased the magnitudes of stress gradients at the interfaces. It was also found that a major effect of plastic deformation is a tendency to produce a more homogeneous stress distribution within the components. The implications of these observations for practical systems are discussed.     

Mechanical properties of ceramics–cement based porous material under impact loading

Cementitious materials and ceramic aggregates used as basic materials, ceramics–cement based porous material (CCPM) has been prepared. Φ100 mm SHPB has been improved by wave shaping techniques, which can guarantee the availability of the tests. Quasi static compression test and impacting compression test have been carried out, the damage process of specimen under loading has been analyzed, and mechanics parameters under different strain rates have been obtained, moreover, based on this, the mechanical properties of CCPM under impact loading, including strength property, deformation property, impacting toughness, have been studied, in addition, the prospect of CCPM’s application has also been discussed. The results indicate that, the quasi static and impact compressive stress–strain curve of CCPM includes a strain plateau, which helps to better absorb energy; the dynamic strength increase factors of CCPM and the natural logarithm of relative strain rate are of a linear relationship; the relationship between the dynamic peak strain increase factors and the related strain rate can be described with an exponential linear, which shows obvious “damage softening” effect; with the increase of average strain rate, the impacting toughness of CCPM gets strengthened continuously and the impact toughness indexes are in a logarithm relationship with strain rate; CCPM is more strain rate sensitive than ordinary cement based composite materials. Thus it can be seen, CCPM possesses the advantageous mechanical properties of both porous materials and ordinary cement based composite materials. Besides, the material is easy to prepare and simple to make. Along with its high plasticity and low density, CCPM has a promising future to perform its potential advantages in engineering, especially in national defense engineering.     

Damage monitoring and analysis of composite laminates with an open hole and adhesively bonded repairs using digital image correlation

High performance composite materials, such as Carbon–Fibre Reinforced Plastic (CFRP) composites, are being increasingly used in aerospace industry, such as fuselage primary structures in Boeing 787 or Airbus 350, where high strength and stiffness are required at minimum weight [1]. The design of composite structures frequently includes discontinuities such as cut-outs for access and fastener holes for joining and they become critical regions under thermo-mechanical loading. Understanding of notched specimen behaviour is necessary for the design of complex structures where parts are mostly connected with bolts and rivets [2]. The effect of these discontinuities on the behaviour of composite materials is an important topic because it causes a relatively large reduction in strength compared to the unnotched laminate [3]. In the first part of the current work, the assessment of the damage process taking place in notched (open-hole) specimens under uniaxial tensile loading was studied. Two-dimensional (2D) and three-dimensional (3D) Digital Image Correlation (DIC) techniques were employed to obtain full-field surface strain measurements in carbon–fibre/epoxy M21/T700 composite plates with different stacking sequences in the presence of an open circular hole. Penetrant enhanced X-ray radiographs were taken to identify damage location and extent after loading around the hole. DIC strain fields were compared to numerical predictions. In the second part of the study, DIC techniques were used to characterise damage and performance of adhesively bonded patch repairs in composite panels under tensile loading. This part of work relates to strength/stiffness restoration of damaged composite aircraft that becomes more important as composites are used more extensively in the construction of modern jet airliners. In the current work, external bonded patches have been studied. Adhesively bonded repairs are the most common type of repair carried out with composite materials [1], [4]. The behaviour of bonded patches under loading was monitored using DIC full-field strain measurements. Location and extent of damage identified by X-ray radiography correlates well with DIC strain results giving confidence to the technique for structural health monitoring of bonded patches.     

Progressive damage modeling for large deformation loading of composite structures

A nonlinear constitutive model for large deformation loading at different strain rate condition was developed to represent tensile progressive damage of the nonlinear large deformation rate dependent behavior of polymer-based composite materials. The material was characterized by using off-axis composite specimens at different strain rates. A new failure criterion was proposed for the analysis of different loading directions and strain rates. Based on a method of combining the nonlinear constitutive theory and the proposed failure criterion for different strain rates, the progressive damage behavior of large deformation composites was represented. The strength of the material was also successfully represented with a single material constant.     

Numerical simulation of ceramic composite armor subjected to ballistic impact

Armor systems made of ceramic and composite materials are widely used in ballistic applications to defeat armor piercing (AP) projectiles. Both the designers and users of body armor face interesting choices – how best to balance the competing requirements posed by weight, thickness and cost of the armor package for a particular threat level. A finite element model with a well developed material model is indispensible in understanding the various nuances of projectile–armor interaction and finding effective ways of developing lightweight solutions. In this research we use the explicit finite element analysis and explain how the models are built and the results verified. The Johnson–Holmquist material model in LS-DYNA is used to model the impact phenomenon in ceramic material. A user defined material model is developed to characterize the ductile backing made of ultra high molecular weight polyethylene (UHMWPE) material. An ad hoc design optimization is carried out to design a thin, light and cost-effective armor package. Laboratory testing of the prototype package shows that the finite element predictions of damage are excellent though the back face deformations are under predicted.     

多层异质复合结构的动力学响应及抗侵彻性能

为研究多层异质复合结构动力学响应及抗侵彻性能,利用霍普金森试验装置,对不同材料排布顺序及含泡沫铝夹芯的多层复合结构进行冲击加载,通过贴在入射杆和透射杆上的应变片测得入射波、反射波、透射波波形,验证数值仿真模型正确性;结合数值模拟,研究不同结构对试件内部应力波传播特性和应力场分布影响规律;依据复合结构动力学响应特征,设计复合靶板并进行抗侵彻试验,分析靶板塑性变形特征及抗侵彻耗能机制;通过数值模拟分析泡沫铝夹芯厚度对防护性能影响。结果表明,装甲钢后置复合结构及含泡沫夹芯结构有助于减缓应力集中,减小陶瓷损伤面积;泡沫铝夹芯过厚难以为靶板变形提供支撑,降低抗侵彻阻力;五种夹芯厚度h=2 mm、h=5 mm、h=10 mm、h=20 mm、h=30 mm中,h=10 mm对应多层异质复合靶防护性能最优。      

Viscoplastic regularization of local damage models: revisited

Local damage models are known to produce pathological mesh dependent results. Regularization techniques are therefore mandatory if local damage models are used for academic research or industrial applications. The viscoplastic framework can be used for regularization of local damage models. Despite of the easy implementation of viscoplasticity, this method of regularization did not gain much popularity in comparison to the non-local or gradient damage models. This work is an effort to further explore viscoplastic regularization for quasi-static problems. The focus of this work is on ductile materials. Two different types of strain rate hardening models i.e. the Power law (with a multiplicative strain rate part) and the simplified Bergström van Liempt (with an additive strain rate part) models are used in this study. The modified Lemaitre’s anisotropic damage model with a strain rate dependency was used in this study. It was found that the primary viscoplastic length scale is a function of the hardening and softening (damage) parameters and does not depend upon the prescribed strain rate whereas the secondary length scale is a function of the strain rate. As damage grows, the effective regularization length gradually decreases. When the effective regularization length gets shorter than the element length numerical results become mesh dependent again. This loss of objectivity can not be solved but the effect can be minimized by selecting a very fine mesh or by prescribing high deformation velocities.     

Multi-scales modelling of dynamic behaviour for discontinuous fibre SMC composites

The requirements of passive security, notably in the transport industry, impose to maximize the dissipation of the energy and to minimize the decelerations undergone by a vehicle and thus passengers due to violent shocks (crash). This paper aims at establishing efficient expected answers towards the preoccupations mainly emanating from transport industry. Currently, the behaviour laws implemented in the dynamic explicit schemes (RADIOSS, PAM-CRASH and LS-DYNA) do not integrate sufficiently the physical aspects in the material degradation, mainly the damage process, their kinetics, the variability and especially the heterogeneity of the composite materials microstructure. This paper deals with the development of a multi-scale predictive model coupling specific experimental methodologies and the micromechanical formulation of damage mechanisms in order to build constitutive laws for discontinuous fibre reinforced composites materials. The developed micromechanical modelling is based on an experimental methodology conducted over a range of strain rates from quasi static to 250 s⁻¹. The latter has enabled identifying local probabilistic damage criterion formulated through the Weibull’s statistical integrating the strain rate effect and describing the progressive interfacial debonding under rapid loading. The developed model has been validated to predict the stiffness reduction and the overall elastic visco-damage behaviour for SMC composite material. The model simulations agree well with high speed tensile tests and confirm that the damage threshold and kinetic in the SMC are mainly strain rate sensitive.     

Tensile and compressive damage coupling for fully-reversed bending fatigue of fibre-reinforced composites

ABSTRACT Due to their high specific stiffness and strength, fibre-reinforced composite materials are winning through in a wide range of applications in automotive, naval and aerospace industry. Their design for fatigue is a complicated problem and a large research effort is being spent on it today. However there is still a need for extensive experimental testing or large safety factors to be adopted, because numerical simulations of the fatigue damage behaviour of fibre-reinforced composites are often found to be unreliable. This is due to the limited applicability of the theoretical models developed so far, compared to the complex multi-axial fatigue loadings that composite components often have to sustain in in-service loading conditions.
In this paper a new phenomenological fatigue model is presented. It is basically a residual stiffness model, but through an appropriate choice of the stress measure, the residual strength and thus final failure can be predicted as well. Two coupled growth rate equations for tensile and compressive damage describe the damage growth under tension–compression loading conditions and provide a much more general approach than the use of the stress ratio R . The model has been applied to fully-reversed bending of plain woven glass/epoxy specimens. Stress redistributions and the three stages of stiffness degradation (sharp initial decline – gradual deterioration – final failure) could be simulated satisfactorily.     

A CONTINUUM MODEL FOR DYNAMIC DAMAGE EVOLUTION OF ANISOTROPIC BRITTLE MATERIALS

This paper is concerned with the development of a computational model for the damage evolution of brittle materials under dynamic loading. Two models for dynamic damage evolution of brittle materials with or without microflaws in general anisotropic damage state are presented; the first one is based on power function of principal tensile stress and the second one is based on damage strain energy release rate. A second-order tensor based elastic–brittle damage model is formulated which is efficient computationally and consistent in its treatment of damage evolution. Measured Weibull strength distribution may be employed to account for flaw size distribution effects on the damage accumulation rate. Methods of computing the accumulated damage of a structural component and their implementation in a finite element program together with some numerical results are presented. Finally, a comparison has been made between the two damage models.     

织物弹道贯穿性能分析计算

纤维织物增强复合材料由于轻质和高冲击损伤容限而在防弹装甲设计及制造中逐渐得到应用,如人体防弹衣和车辆防护装甲。但是尚无较好的方法直接计算复合材料防弹特性,其中困难在于复合材料弹道冲击过程中的应变率效应和冲击破坏机理至今没有被揭示。解决问题的第一步是建立复合材料增强相(即织物)防弹特性计算方法。提出基于纤维力学性质应变率效应的织物弹道冲击破坏分析模型,计算不同面密度织物靶体在弹道贯穿过程中的弹体剩余速度,由此反映靶体防弹特性。用本文中提出的简单算法预测的结果与实测结果在靶体厚度不大时极为接近,而且也有可能将其扩展到纤维织物增强复合材料防弹性质的计算。     

On the drop-weight testing of alumina/aluminum laminated composites

Laminated composites with ceramic front layers and metallic or composite backing layers have gained attractiveness as lightweight armours, as they exhibit the same ballistic performance with lower areal densities as compared to steels. Drop-weight testing (DWT) has potential for evaluating the low velocity impact behaviour of materials. This testing gives significant ideas and information about failure mechanisms and behaviour of materials under low velocity impact. In this study, DWT of alumina/aluminum laminated composites was done in order to investigate the effects of lamination type, density with respect to area and mechanical property of backing material on the low velocity ballistic performance of these composites. The experimental results showed that the laminated composite with ceramic front layer and aged-aluminum alloy as backing layer was the most effective among different investigated specimens against low velocity impact loads.     

Large-Deformation Constitutive Theories for Structural Composites: Rate-Dependent Concepts and Effect of Microstructure

Abstract:  Polymer-based composite materials are widely used in applications subjected to a variety of loading types, including shock and impact loading in the range of hundreds of strain per second. The behaviour of composite laminates loaded at those rates is typically nonlinear and may involve rather large strains to failure. In the present study, the large-deformation characteristics and constitutive representations of structural composites were investigated as functions of strain rate and temperature. A plain-weave vinyl ester composite material was selected for the study. Tensile tests of off-axis coupon specimens were conducted over several orders of strain rates and limited change of temperatures. A three-parameter constitutive model was proposed to model the large-deformation stress–strain relationship. The constitutive model was then used to predict the material response at different strain rates. The model predictions were verified by a different set of tests. The basic concepts and methodologies involved in reducing such data to constitutive equations that can be used in commercial computational codes to enable structural analysis in the presence of large-strain progressive damage under dynamic loading is discussed.     

A simple one-dimensional approach to modelling ceramic composite armour defeat

This work develops a simple set of models for the perforation of ceramic composite armour, which highlight the essential physical processes and illustrate approximately the dependency of ballistic resistance on physical properties and impact parameters. The major features of ceramic composite armour failure (viz. fracture conoid formation, dishing failure of thin backing plates, perforation of thick packing plates, and projectile erosion) are combined with a lumping of masses to treat material acceleration to produce simple models which allow computations on ceramic targets with both thin and thick metallic backings. Calculations are compared with a broad range of empirical data and are also used to discuss aspects of the interaction of penetrators with ceramic composite armours. The goos correlation of models with experiment demonstrates the usefulness of the present approach for studying ceramic composite armour defeat.     

损伤材料的动力响应特性

研究了工程材料在动力载荷下损伤演化的计算模型。提出了一般材料在各向异性损伤状态下的两种动力损伤模型。第一种以有效应力的等效值的幂函数为基础 ,第二种以损伤应变能释放率为基础。通过数值分析研究了损伤结构元件的动力响应及损伤材料的动力特性。说明了结构元件中损伤发展的分析方法和它们的有限元程序的执行过程。该研究表明 :损伤结构的频谱下移 ,损伤材料的阻尼比变高 ,响应的振幅明显增加 ,损伤结构可能发生由于损伤发展引起的共振。     

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

This paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows:

• A unified treatment for the analysis and implicit time integration of thermo‐elasto‐viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework.
• An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated.
• An operator split‐based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo‐elasto‐viscoplastic problem.
• The possibility to couple any hardening law, including rate‐dependent models, with any damage model that fits into the present framework.

All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact and metal‐forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS‐MN ²L, University of Liège, Belgium) named Metafor.Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental and Numerical Analysis of Damage in Woven GFRP Composites Under Large-deflection Bending

Textile-reinforced composites such as glass fibre-reinforced polymer (GFRP) used in sports products can be exposed to different in-service conditions such as large bending deformation and multiple impacts. Such loading conditions cause high local stresses and strains, which result in multiple modes of damage and fracture in composite laminates due to their inherent heterogeneity and non-trivial microstructure. In this paper, various damage modes in GFRP laminates are studied using experimental material characterisation, non-destructive micro-structural damage evaluation and numerical simulations. Experimental tests are carried out to characterise the behaviour of these materials under large-deflection bending. To obtain in-plane shear properties of laminates, tensile tests are performed using a full-field strain-measurement digital image correlation technique. X-ray micro computed tomography (Micro CT) is used to investigate internal material damage modes – delamination and cracking. Two-dimensional finite element (FE) models are implemented in the commercial code Abaqus to study the deformation behaviour and damage in GFRP. In these models, multiple layers of bilinear cohesive-zone elements are employed to study the onset and progression of inter-ply delamination and intra-ply fabric fracture of composite laminate, based on the X-ray Micro CT study. The developed numerical models are capable to simulate these features with their mechanisms as well as subsequent mode coupling observed in tests and Micro CT scanning. The obtained results of simulations are in agreement with experimental data.     

Numeral modeling of fracture failure of recycled aggregate concrete beams under high loading rates

Fracture tests of recycled aggregate concrete (RAC) beams of different sizes were conducted under high loading rates. In order to characterize the effect of high loading rate on the behavior of RAC beams, two new material models were used together with the commercial finite element software \(\hbox {ABAQUS}^{\mathrm{R}}\). One model is a viscoelastic model that can predict the increase of stiffness (modulus of elasticity) of RAC with increasing loading rate, and the other model is a multiphase composite model that can determine the effective stiffness of RAC taking into account the special internal structure of recycled aggregate. Two different cases were considered in the numerical simulation. Case 1 is for fixed beam size under different loading rates, and Case 2 is for fixed loading rate with different beam sizes. For Case 1, the simulation results of the maximum loads under three different strain rates agreed with test data quite well. The Force-CMOD curves of the numerical simulation and test data showed similar trends. The higher the strain rates, the wider the high stresses spread in the crack propagation zone. The good agreements with the test data indicated that the two new material models can characterize the effect of high loading rate on RAC beams very well. For Case 2, three beam sizes and one loading rate was studied. The post-peak Force versus CMOD curves from the simulation follow the same trend of the test data. The stress distributions in the beams of different sizes are similar. On the other hand, the maximum loads predicted by the numerical model did not agree very well with test data. This is due to the fact that the maximum forces of RAC notched beams exhibited size effect, which was not considered in the fracture criteria adopted in \(\hbox {ABAQUS}^{\mathrm{R}}\) and not in the two new material models. This will be a topic for future research.     

Ballistic impact performance of an armor material consisting of alumina and dual phase steel layers

Utilization of a ceramic front layer provides an improvement in the ballistic efficiency of monolithic metallic materials. In the current paper, the ballistic behavior of laminated composite having alumina front and dual phase steel backing layers was studied using 7.62 mm armor piercing (AP) projectiles under normal impact. The variables used were martensite content of the backing layer and the areal density of the composite. Experimental results showed that utilization of a 6 mm thick alumina front layer which was bonded to dual phase steel enhanced the ballistic resistance of the dual phase steel remarkably.