A rate-dependent constitutive equation for 5052 aluminum diaphragms

In this article, both experimental and numerical approaches are conducted to present a constitutive equation for 5052 aluminum diaphragms under quasi-static strain rate loadings. For this purpose the stress–strain curves at different strain rates are obtained using tensile tests. Brittle behavior during tensile tests is observed due to samples thin thicknesses. Employing Johnson–Cook constitutive equation no yields in reasonable agreement with these tensile tests results. Therefore, developing a more suitable constitutive equation for aluminum diaphragms is taken into consideration. This equation is then implemented into the commercial finite element software, ABAQUS, via a developed user material (UMAT) subroutine utilizing von Mises plasticity theory and an own solution algorithm. A single-element pathological test method is adopted to show the well-development of the UMAT subroutine. In order to verify the proposed constitutive equation for precision predicting of mechanical behavior, a bulge test is performed in which demonstrates a good agreement between experimental and numerical results.     

Numerical implementation of an elastic-viscoplastic constitutive model to simulate the mechanical behaviour of amorphous polymers

Due to their high deformation capabilities, polymeric materials are widely used in several industries. However, polymers exhibit a complex behaviour with strain rate, temperature and pressure dependencies. Numerous constitutive models were developed in order to take into account their specific behaviour. Among these models, the ones proposed by Richeton et al Polymer 46:6035–6043 (2005a), Polymer 46:8194–8201 (2005b) seem to be particularly suitable. They proposed expressions for the Young modulus and the yield stress with strain rate and temperature dependence. Moreover, these models were also implemented in a finite elastic-viscoplastic deformation approach using a flow rule based on thermally activated process. The increase of computational capabilities allowed simulating polymer forming processes using finite element (FE) codes. The aim of the study is to implement the proposed constitutive model in a commercial FE code via a user material subroutine. The implementation of the model was verified using compressive tests over a wide range of strain rates. Next, FE simulations of an impact test and of a plane strain forging process were carried out. The FE predictions are in good agreement with the experimental results taken from the literature.     

A temperature- and strain-rate-dependent isotropic elasto-viscoplastic model for glass-fiber-reinforced polyurethane foam

The primary aim of the present study is to provide a new constitutive model and its computational procedure for a glass-fiber-reinforced polyurethane foam (RPUF) subjected to various cryogenic temperatures and compressive loading rates. A Frank–Brockman-type isotropic elasto-viscoplastic model was introduced to describe the hardening and softening phenomena of RPUF under compressive loads. In addition, the increase of the yield strength and plateau according to the change of temperature and strain rates was demonstrated using the given constitutive model. The introduced numerical model was transformed as an implicit form and was implemented into a user-defined subroutine of commercial finite element analysis (FEA) code, i.e., ABAQUS UMAT. Based on the developed material library, the complex elasto-plastic behavior of RPUF under various cryogenic temperatures and strain rates was numerically estimated. The variation of material internal variables, such as hardening and softening control parameters, was quantitatively investigated, and the temperature- and strain-rate-dependent empirical formulae, namely, a polynomial multiple regression model, were proposed. Finally, the simulation results were compared with a series of compressive test results to validate the proposed method. On using the developed numerical method, it might be feasible to predict the unknown stress–strain behavior of RPUF under arbitrary severe environments.     

Finite element modeling of ballistic impact on multi-layer Kevlar 49 fabrics

This paper presents a material model suitable for simulating the behavior of dry fabrics subjected to ballistic impact. The developed material model is implemented in a commercial explicit finite element (FE) software LS-DYNA through a user defined material subroutine (UMAT). The constitutive model is developed using data from uniaxial quasi-static and high strain rate tension tests, picture frame tests and friction tests. Different finite element modeling schemes using shell finite elements are used to study efficiency and accuracy issues. First, single FE layer (SL) and multiple FE layers (ML) were used to simulate the ballistic tests conducted at NASA Glenn Research Center (NASA-GRC). Second, in the multiple layer configuration, a new modeling approach called Spiral Modeling Scheme (SMS) was tried and compared to the existing Concentric Modeling Scheme (CMS). Regression analyses were used to fill missing experimental data – the shear properties of the fabric, damping coefficient and the parameters used in Cowper-Symonds (CS) model which account for strain rate effect on material properties, in order to achieve close match between FE simulations and experimental data. The difference in absorbed energy by the fabric after impact, displacement of fabric near point of impact, and extent of damage were used as metrics for evaluating the material model. In addition, the ballistic limits of the multi-layer fabrics for various configurations were also determined.     

The effect of heat developed during high strain rate deformation on the constitutive modeling of amorphous polymers

An adiabatic constitutive model is proposed for large strain deformation of polycarbonate (PC) at high strain rates. When the strain rate is sufficiently high such that the heat generated does not have time to transfer to the surroundings, temperature of material rises. The high strain rate deformation behavior of polymers is significantly affected by temperature-dependent constants and thermal softening. Based on the isothermal model which first was introduced by Mulliken and Boyce et al. (Int. J. Solids Struct. 43:1331-1356, 2006), an adiabatic model is proposed to predict the yield and post-yield behavior of glassy polymers at high strain rates. When calculating the heat generated and the temperature changes during the step by step simulation of the deformation, temperature-dependent elastic constants are incorporated to the constitutive equations. Moreover, better prediction of softening phenomena is achieved by the new definition for softening parameters of the proposed model. The constitutive model has been implemented numerically into a commercial finite element code through a user material subroutine (VUMAT). The experimental results, obtained using a split Hopkinson pressure bar, are supported by dynamic mechanical thermal analysis (DMTA) and Decompose/Shift/Reconstruct (DSR) method. Comparison of adiabatic model predictions with experimental data demonstrates the ability of the model to capture the characteristic features of stress–strain curve of the material at very high strain rates.     

Characterization and constitutive modeling of stress-relaxation behavior of Poly(methyl methacrylate) (PMMA) across the glass transition temperature

Characterizing the large strain behavior of Poly(methyl methacrylate) (PMMA) across its glass transition temperature is essential for modeling hot embossing. Its mechanical properties vary significantly across the glass transition as well as with strain rate. Several previous models have attempted to capture this behavior with limited success, and none have considered stress relaxation. In this work, stress relaxation experiments are conducted on PMMA at various temperatures spanning the glass transition. The experimental data is then used to develop a new constitutive model. As with earlier models for thermoplastics around the glass transition, the material model consists of two resistances: intermolecular and network. The key advantage of the new model is that the network resistance is represented through an 8-chain hyperelastic model in parallel with a ROuse LInear Entangled POLYmer (Rolie-Poly) element. The structure of the network interactions captures the strain hardening at temperatures less than glass transition and the melt behavior at temperatures greater than glass transition to greatly improve stress relaxation predictions. Strain softening is introduced in the intermolecular branch to predict the stress at small strains. Glass transition is described through temperature dependent material properties. Results have been encouraging for the model’s ability to capture stress relaxation behavior from temperatures 15° below to 25° above glass transition. In addition, it can capture the relaxation behavior at both large and small strains as well as with varying strain rates. This ability to capture stress relaxation suggests it will greatly improve finite element model predictions for hot embossing with PMMA.     

Mechanical response of a soft rubber compound compressed at various strain rates

Rate-dependent material constitutive behavior models are needed in numerical simulations of shock-mitigation structures. In this research, compressive stress–strain response of a soft rubber compound is obtained experimentally at quasi-static, intermediate and high strain rates under uniaxial-stress and uniaxial-strain loading states. Kolsky bars with modifications for characterizing soft materials and a long Kolsky bar are used to conduct the dynamic experiments, while an MTS load frame is used for conducting experiments at quasi-static rates. Compression experiments are conducted at each decade in the strain-rate scale without any gap typically seen in the intermediate range. The experimental results show significant strain-rate effects on the mechanical behavior of this soft material, which are summarized via a rate-dependent constitutive model.     

An inverse approach to determine the constitutive model parameters from axial crushing of thin-walled square tubes

Knowledge of the behaviour of structural components is essential for their design under crash consideration. Constitutive models describe their material behaviour in finite element (FE) codes. These constitutive models are in relation to the material parameters which have to be determined. The strain rates commonly observed in crash events are in the range of 0–500 s^-1. Classic experimental devices such as Hopkinson’s bars do not easily cover this range of strain rates. An inverse numerical approach based on the experimental quasi-static and dynamic axial crushing of thin-walled square tubes has therefore been developed to determine the constitutive model’s parameters. The inverse method is applied in this paper in two stages to determine the power type elastic–plastic constitutive model’s parameters and the Cowper–Symonds constitutive model’s parameters. The identified power law is compared with the results obtained by quasi-static tensile tests and shows that the identified parameters are intrinsic to the material behaviour. The Cowper– Symond’s parameters identified by this method are then used in FE simulation to predict the dynamic response of the same square tube subjected to bending loading. The results obtained show a good correlation between the experimental and numerical results.     

温度、应变率对航空PMMA压缩力学性能的影响研究

本文利用INSTRON试验机和分离式Hopkinson压杆测试了航空有机玻璃在试验温度为299K～373K之间,两种准静态应变率(10-3,10-1 1/s)和一种动态应变率(550 1/s)下的压缩力学行为.试验结果表明:在准静态载荷下,随着温度的升高,材料的弹性模量和流动应力减小,在应变率为10-1 1/s时表现出明显的应变软化行为;在高应变率(550 1/s)下,随着温度的升高,材料的流动应力逐渐减小而破坏应变增大,当温度超过333K时也有应变软化现象发生;在相同温度下,随着应变率的升高,材料的流动应力增大,但破坏应变减小.通过观察变形后试样的形貌,可以认为试样内部的微裂纹是应变软化的主要原因.最后,ZWT粘弹性本构模型被用来对试验数据进行拟合,结果表明该模型能够较好地预测这种材料在应变8%以内的力学行为.     

空调塑料材料的碰撞失效模拟研究

研究空调内机塑料材料ABS-121H在跌落工况下的力学行为。通过准静态、动态拉伸力学实验和失效实验,分别建立了不同应变率下材料弹塑性模型及LS-DYNA软件的GISSMO失效模型,并通过整机零部件实验及仿真对材料弹塑性模型和失效模型准确性进行验证。结果表明:考虑应变率效应的材料弹塑性模型可以准确反映结构的加速度和刚度,GISSMO失效模型可以准确预测材料复杂应力状态下的断裂失效行为。该研究为空调跌落仿真的材料模型建立提供参考。     

双轴受压状态下的高延性纤维增强水泥基复合材料本构模型

基于Darwin和Pecknold考虑混凝土双轴力学行为的方法,建立一个同时考虑双轴受压状态下非线性力学行为和抗压强度变化的高延性纤维增强水泥基复合材料(ECC)二维正交各向异性本构模型。在因双轴加载而产生的正交各向异性的2个方向上引入等效单轴应变,建立非线性应力-等效单轴应变关系以考虑ECC的双轴非线性行为,并采用一条双轴强度包络线确定2个方向上的抗压强度。推导模型的显式数值算法,编写包含该算法的用户自定义材料子程序UMAT,并嵌于有限元计算程序ABAQUS v6.14中。通过对两组不同配合比的ECC试件在不同应力比下的双轴受压加载试验进行数值分析验证本模型的有效性。数值计算得到的主压应力方向上的应力-应变曲线及预测的抗压强度与试验结果吻合较好,表明该文提出的本构模型能够有效地预测ECC在双轴受压状态下的非线性力学行为和破坏强度。     

Finite element analysis of combined forming processes by means of rate dependent ductile damage modelling

Sheet metal forming is an inherent part of todays production industry. A major goal is to increase the forming limits of classical deep-drawing processes. One possibility to achieve that is to combine the conventional quasi-static (QS) forming process with electromagnetic high-speed (HS) post-forming. This work focuses on the finite element analysis of such combined forming processes to demonstrate the improvement which can be achieved. For this purpose, a cooperation of different institutions representing different work fields has been established. The material characterization is based on flow curves and forming limit curves for low and high strain rates obtained by novel testing devices. Further experimental investigations have been performed on the process chain of a cross shaped cup, referring to both purely quasi-static and quasi-static combined with electromagnetic forming. While efficient mathematical optimization algorithms support the new viscoplastic ductile damage modelling to find the optimum parameters based on the results of experimental material characterization, the full process chain is studied by means of an electro-magneto-mechanical finite element analysis. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine into the commercial finite element package LS-DYNA.     

A modified Johnson–Cook constitutive model for Mg–Gd–Y alloy extended to a wide range of temperatures

In this paper, a new phenomenological and empirically based constitutive model was proposed to change the temperature term in the original Johnson–Cook constitutive model. The new model can be used to describe or predict the stress–strain relation of the metals deformed over a wide range of temperatures even though the current temperatures were lower than the reference temperature. Based on the impact compression data obtained by split Hopkins pressure bar technique, the material constants in the new model can be experimentally determined using isothermal and adiabatic stress–strain curves at different strain rates and temperatures. Good agreement is obtained between the predicted and the experimental stress–strain curves for a hot-extruded Mg–10Gd–2Y–0.5Zr alloy at both quasi-static and dynamic loadings under a wide range of temperatures ever though the current temperatures were lower than the reference temperature.     

Investigating the static and dynamic tensile mechanical behaviour of polymer‐bonded explosives

The tensile properties of a polymer‐bonded explosive (PBX) were systematically studied by using quasi‐static and dynamic experiments. A non‐linear constitutive relation was developed to describe the tensile behaviour of the PBX. The tensile properties of the PBX under different strain rates and temperatures were measured in quasi‐static tests. The tensile behaviour of the PBX was found to exhibit high strain rate and strong temperature dependence, attributable to the large fraction of the polymer binder. To obtain the rational dynamic tensile results, a modified split Hopkinson tensile bar (SHTB) setup was designed such that the specimens were in dynamic stress equilibrium and deformed homogeneously at nearly constant strain rates. To characterise the viscoelastic behaviour, the master modulus curve was derived from the tensile stress relaxation tests at different temperatures. The non‐linear constitutive model was implemented in ABAQUS to predict the tensile behaviour of the PBX. The computational results were found to be in good agreement with the experimental results.     

Damage characterization in non-isothermal stretching of acrylics. Part II: Experimental validation

Influence of temperature and strain rate on damage accumulation and large deformation behavior of acrylics was investigated under conditions similar to actual polymer processing. Poly(methyl methacrylate) (PMMA) samples were stretched to large strains at different rates under transient thermal conditions. During testing, specimens were cooled down from temperatures above glass transition temperature (θ_g) to temperatures well-below θ_g inducing a transition from rubbery state to solid state. Contrary to common practice of studying thermo-mechanical coupling in terms of adiabatic heating; in proposed experimental study, temperature effect on mechanical response of material was emphasized by externally intervening temperature variation within specimen. An improved version of dual-mechanism constitutive model presented in Part I [Gunel, E.M., Basaran, C., 2010. Damage characterization in non-isothermal stretching of acrylics. Part I: Theory. Mechanics of Materials] was proposed to predict thermo-mechanical response of amorphous polymer below and above θ_g. Applicability of proposed constitutive model for the specific case of non-isothermal stretching of PMMA at different test conditions was demonstrated by incorporating it into a finite element scheme. Constitutive model was reasonably accurate to capture observed temperature-displacement-force history in experimental study. Damage evolution under different testing conditions was studied in terms of irreversible thermal and mechanical entropy production.     

Measurement and prediction of compressive properties of polymers at high strain rate loading

Strain-rate effect is widely recognized as a crucial factor that influences the mechanical properties of material. Despite the acknowledge importance, the understanding of how such factor interact with the sensitivity of the polymers in terms of mechanical properties is still less reported. In this study, an experimental technique, based on the compression split Hopkinson pressure bar, was introduced to perform high strain rate testing, whereas, a conventional universal testing machine was used to perform static compression testing, to experimentally investigate the independent and interactive effects of strain rates towards mechanical properties of various polymers. Based on the experimental results, we parameterized two equation models, which were used to predict the yield behavior of tested polymer samplings. The experimental results indicate that, the yield stress, compression modulus, compressive strength, strain rate sensitivity and strain energy increased significantly with increasing strain rates for all tested polymers. Meanwhile, the yield strain and the thermal activation volume exhibit contrary trend to the increasing strain rates. Interestingly, the proposed constitutive models were almost agreed well with experimental results over a wide range of strain rate investigated. Of the three polymers, polypropylene shows the highest strain rate sensitivity at static and quasi-static region. On the other hand, at dynamic region, polycarbonate shows the highest strain rate sensitivity than that of polypropylene and polyethylene. Overall, both experimental and numerical models proved that the mechanical properties of polymer show significant sensitivity and dependency towards applied strain rates up to certain extent.     

三维四向编织复合材料界面损伤机理数值分析

考虑界面脱粘表面压应力下摩擦力对材料界面力学性能的影响,建立损伤-摩擦相结合的界面本构模型,编写用户材料子程序VUMAT,实现其在有限元软件ABAQUS中的嵌入。基于周期性胞元分析思想,在单胞模型中纤维束/基体、纤维束/纤维束分界面引入界面单元,结合损伤-摩擦相结合的界面本构模型,建立含界面相三维四向编织复合材料的细观有限元模型。模拟典型载荷下界面损伤的起始和扩展过程,分析界面应力传递和界面破坏机理,研究界面性能对复合材料宏细观力学性能的影响规律,为实现三维四向编织复合材料界面性能优化设计和控制提供参考。      

Impact behavior and constitutive model of nanocrystalline Ni under high strain rate loading

To investigate mechanical properties and deformation mechanisms of nanocrystalline materials under high strain rate, dynamic impact tests for nanocrystalline Ni bulk prepared by high-energy ball milling combined with compaction and hot-pressure sintering were carried out under different high strain rates on Split Hopkinson bar. Compared with the testing results under quasi-static strain rate, the nanocrystalline Ni has higher strength under high strain rate. Meanwhile, the impact stress–strain curves exhibit rate-dependence strength and light strain hardening behavior. Subsequently, a mechanism of dislocation gliding in combination of grain boundary sliding was discussed and a constitutive model was built under high strain rate loading based on the mechanism. The predictions of the constitutive model under high strain rates show good agreements with the experimental data. Finally, the properties of the nanocrystalline Ni were discussed in detail.     

Simulating Initial and Progressive Failure of Open-Hole Composite Laminates under Tension

A finite element (FE) model is developed for the progressive failure analysis of fiber reinforced polymer laminates. The failure criterion for fiber and matrix failure is implemented in the FE code Abaqus using user-defined material subroutine UMAT. The gradual degradation of the material properties is controlled by the individual fracture energies of fiber and matrix. The failure and damage in composite laminates containing a central hole subjected to uniaxial tension are simulated. The numerical results show that the damage model can be used to accurately predicte the progressive failure behaviour both qualitatively and quantitatively.