A GENERAL CONSTITUTIVE RELATION FOR FATIGUE CRACK GROWTH ANALYSIS OF METAL STRUCTURES

Crack growth rate curves are the fundamental material property for metal structures under fatigue loading. Although there are many crack growth rate curves available in the literature, few of them showed the capability to explain various special phenomena observed in tests. A modified constitutive relation recently proposed by McEvily and his co-workers showed very promising capability. This modified constitutive relation is further generalized by (1) introducing an unstable fracture condition; (2) defining a virtual strength to replace the yield stress; and (3) defining an overload and underload parameter. The performances of this general constitutive relation for fatigue crack growth is extensively studied and it is found that this general constitutive relation is able to explain various phenomena observed with particular strong capability on load sequence effect.

Dynamic Response Analysis of Bird Strike on Aircraft Windshield Based on Damage-modified Nonlinear Viscoelastic Constitutive Relation

Damage-modified nonlinear viscoelastic constitutive equation and failure criterion are introduced and the three-dimensional incremental forms are deduced based on the updated Lagrangian approach. A simple tensile test model and a split Hopkinson pressure bar model are built to verify the accuracy of the subroutine implemented within the non-linear finite element program LS-DYNA. A numerical model of bird strike on windshield is established to study the responses of windshield under three different bird velocities at three sites. The bird is represented by a cylinder with a hemisphere at each end and the contact-impact coupling algorithm is used in this study. It is found that the implemented subroutine can properly describe the mechanical behavior of polymethyl methaerylate under low and high strain rates and large deformation, and can be used validly.

STUDY ON DYNAMIC CONSTITUTIVE RELATIONS FOR CONCRETE WITH FINITE DEFORMATION

The differences between finite deformation and infinitesimal deformation are discussed. They are exercised on elasto-viscoplastic constitutive relations of concrete. Then, a rate-dependent mechanics model was presented on the basis of Ottosen's four-parameter yield criterion, where different loading surface transferring laws were taken into account, when material was in hardening stage or in softening stage, respectively. The model is well established, so that it can be applied to simulate the response of concrete subject to impact loading. Green-Naghdi stress rate was introduced as objective stress rate. Appropriate hypothesis was postulated in accordance with many experimental results, which could reflect the mechanical behaviour of concrete with large deformation. Available thoughts as well as effective methods are also provided for the research on related engineering problems.

Constitutive model depending upon temperature and strain rate of carbon constructional quality steels

The basic factors relating to the rheological stress in the constitutive equations were introduced.Carbon constructional quality steels were regarded as a kind of elastic-viscoplastic materials under high temperature and the elastic-viscoplastic constitutive models were summarized.A series of tension experiments under the same temperature and different strain rates,and the same strain rate and different temperatures were done on 20 steel,35 steel and 45 steel.52 groups of rheological stress-strain curves were obtained.The experimental results were analyzed theoretically.The rheological stress constitutive models of carbon steels were built combining the strong points of the Perzyna model and Johnson-Cook model.Comparing the calculation results conducted from the model with the experiment results,the results proves that the model can reflect the temperature effect and strain rate effect of carbon constructional quality steels better.

Study on the Dynamic Behavior of Tungsten Alloy at Strain Rates up to 5 000 s^(-1)

The dynamic stress-strain curves of 93% tungsten (W) alloy in the forged state at strain rates up to (5 000 s^(-1)) and in the temperature range from 223 K to 473 K were measured with the split Hopkinson pressure bar (SHPB) technique. Based on the above experimental data a dynamic constitutive equation considering the effects of strain rate, temperature and the special microstructure of such a kind of W-alloy was proposed. The numerical simulation for the experimental process with this constitutive equation was also carried out, the results show that the constitutive relationship constructed in this paper is very satisfactory for representing the dynamic responsive behavior of material..

Dependence of flow strength and deformation mechanisms in common wrought and die cast magnesium alloys on orientation,strain rate and temperature

The controlling plastic deformation mechanisms(i.e.slip or twinning)and the structural crash performance of Mg alloys are strongly influenced by loading mode,texture and microstructure.This paper summarizes the main results from an experimental program to assess these effects for commercial Mg alloy extrusions(AM30 and AZ31),sheet(AZ31),and high pressure die castings(HPDC,AM50 and AM60).Uniaxial tensile and compressive tests were performed over a wide range of strain rate and temperature(i.e.0.00075–2800 s^(−1) and 100℃ to−150℃)using conventional servo-hydraulic and high-strain-rate universal test machines and a split-Hopkinson-bar(SHB)apparatus.In primarily-slip-dominant deformation,the true stress–strain curves showed approximate power-law behavior,and the effects of strain rate and temperature on yield strength could be approximately described by constitutive equations linearly dependent on the rate parameter,Tln(5.3×10^(7)/ɛ˙)where T is test temperature in Kelvin andɛ˙is strain rate in s^(−1).In primarily-twin-dominant deformation,the effects of strain rate and temperature on yield and initial flow stress were negligible or small from quasi-static to 2800 s^(−1) owing to the athermal characteristics of mechanical twinning;the effects may become more pronounced with exhaustion of twinning and increasing proportion of slip.

CYCLIC VISCOPLASTIC DESCRIPTION FOR THE MEAN STRAIN EFFECT

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Dynamic necking of a near α titanium alloy at high strain rates:Experiments and modelling

The tensile behaviour of near a Ti3Al2.5 V alloy,conceived for applications in aerospace and automotive engineering,is characterized from quasi-static to high strain rates.The material is found to present noticeable strain rate sensitivity.The dynamic true strain rate in the necking cross-section reaches values up to ten times higher than the nominal strain rate.It is also observed that beyond necking the dynamic true stress-strain curves present limited rate dependence.The experimental results at different strain rates are used to determine a suitable constitutive model for finite element simulations of the dynamic tensile tests.The model predicts the experimentally macroscopic force-time response,true stress-strain response and effective strain rate evolution with good agreement.

Elasto-plastic constitutive model of aluminum alloy foam subjected to impact loading

A multi-parameter nonlinear elasto-plastic constitutive model which can fully capture the three typical features of stress-strain response, linearity, plasticity-like stress plateau and densification phases was developed. The functional expression of each parameter was determined using uniaxial compression tests for aluminum alloy foams. The parameters of the model can be systematically varied to describe the effect of relative density which may be responsible for the changes in yield stress and hardening-like or softening-like behavior at various strain rates. A comparison between model predictions and experimental results of the aluminum alloy foams was provided to validate the model. It was proved to be useful in the selection of the optimal-density and energy absorption foam for a specific application at impact events.

Compression behavior and constitutive model establishment of fly ash cenosphere/polyurethane aluminum alloy syntactic foam

The aluminum matrix syntactic foam was fabricated by pressure infiltration technique,and the filling material is syntactic foam material with fly ash cenosphere as the main component and polyurethane foam as the binder.Split Hopkinson pressure bar(SHPB)dynamic compression and quasi-static tests were carried out to examine the compressive response of syntactic foam in this study.Then the dynamic constitutive model was established.Results show that the compressive stress-strain curve of syntactic aluminum foam is similar to that of other metallic foam materials:both kinds of aluminum matrix syntactic foams have strain rate effect,and the syntactic foam has higher compressive strength and energy absorption than the same density aluminum foams.However,due to the different sizes of cenospheres,the dynamic compression results of two kinds of syntactic foams are different,and the energy absorption effect of syntactic foam with small size under dynamic impact is the best.In the range of strain rate and density studied experimentally,the curves of constitutive model fit well with the curves of experimental data.

CONSTITUTIVE MODEL AND DYNAMIC MECHANICAL PROPERTIES OF GLASS-CLOTH/EPOXY LAMINATES AT DIFFERENT TEMPERATURES

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高温高应变率下钛合金Ti6Al4V的动态力学行为及本构关系

采用分离式霍普金森压杆实验技术,研究了钛合金Ti6Al4V在温度为25~800℃、应变速率为2 000~7 000 s-1的冲击压缩下的动态力学行为和微观组织演变,分析了其力学响应的温度依赖性和应变率敏感性,构建了可准确表征材料塑性流动行为的修正Johnson-Cook模型。结果表明,Ti6Al4V具有显著的应变硬化、应变率强化、应变率增塑和温度软化效应。随着加载温度和应变率的升高,材料的应变硬化效应减弱。温度敏感性随加载温度的升高而显著降低。应变率敏感性因子与加载温度呈负相关,随真实应变的增大呈下降趋势。高温高应变率下细小等轴α相、拉长型α相和块状α相取代初始等轴α相成为Ti6Al4V微观组织的典型特征。考虑率-温耦合作用和绝热温升影响的修正Johnson-Cook模型能够准确地预测Ti6Al4V的塑性流动应力-应变响应。

不同密度硬质聚氨酯泡沫的力学性能和本构关系

目的不同密度的硬质聚氨酯泡沫(RPUF)适用于不同的工程应用,通过对不同密度RPUF力学性能开展研究,并对现有的本构模型加以修正,得到材料真实的本构关系。方法通过开展不同密度RPUF材料的准静态压缩实验(0.001 s^(−1))及不同加载速率(100~1000 s^(−1))下的动态压缩力学性能实验,得到材料的应力-应变曲线,在此基础上分析RPUF材料的密度效应及应变率敏感性,得到其真实本构关系。结果RPUF材料力学性能受到密度和应变率的耦合影响,随着密度以及应变率的增大,RPUF材料的屈服应力呈指数函数形式增大;给出了RPUF材料屈服应力与应变率及密度之间的函数关系式。结论得到了基于实验数据以及横向惯性效应修正后的Sherwood-Frost模型(M-S-F模型),研究结果可为RPUF材料在抗冲击方面的工程应用提供指导。

Investigating the mechanical properties of cortical bone under dynamic torsional loading

Bone is a multi-phase,non-homogeneous material that exhibits strain rate sensitivity,and it may fail under compression,tension,torsion,or a combination of these loading.The mechanical properties of cortical bone with strain rate effect under compression and tension have been obtained through the application of the split Hopkinson pressure/tension bar technique,but no such studies have been reported for determining the strain rate behavior properties of bony materials under torsion.In this study,the shear stress-strain curves with the rate-dependent cortical bone subjected to dynamic torsional loading were first obtained using a torsional split Hopkinson bar system.Based on the experiments,an improved mathematical model consisting of elastic,viscoelastic,and viscoplastic components was used to identify the material parameters of the cortical bone.Detailed material properties are derived through constitutive relations.The results may assist researchers in developing more accurate models of cortical bone behavior under different load conditions.

TC4钛合金电致塑性本构方程建立

采用自行设计的绝缘夹具对TC4钛合金板材进行了电致塑性单向拉伸试验。基于对照试验的方法,以无脉冲电流且不同温度条件作为参照,与同等温度条件下脉冲电流加热情况进行对比,以探索电流参数对TC4钛合金电致塑性效应和力学性能的影响规律。结果表明:在试验研究范围内,脉冲电流的占空比主要影响材料的温度变化,脉冲电流密度对TC4钛合金的电致塑性起主导地位,脉冲电流作用下的TC4钛合金材料抗拉强度大幅下降,塑性提高。基于Johnson-Cook模型和Arrhenius方程建立了耦合温度和脉冲电流密度的TC4钛合金电致塑性本构方程,并进行了验证。

Kevlar29纱线动态拉伸力学性能与本构方程

为了能够清晰地表征芳纶纱线在不同应变率下的力学行为,进行了Kevlar29纱线的准静态和动态拉伸试验,结合分离式霍普金森拉杆理论和运动目标追踪法,获得了Kevlar29纱线在不同应变率下的应力-应变曲线,分析了纱线动态拉伸的变形与断裂过程,揭示了Kevlar29纱线力学性能的应变率效应;通过最小二乘法拟合得到了基于纱线应变率效应的黏弹性本构方程,分析了三元件和五元件本构模型的差异及适用性。结果表明:随着应变率升高,Kevlar29纱线的断裂应变减小,拉伸强度和韧性先增大后减小,拉伸模量先增大后趋于稳定;五元件黏弹性本构模型能够较好地表征纱线力学性能的应变率效应。

高温下多主元合金的动态变形行为与本构建模

为加速多主元合金在航空工业领域的应用,将航空发动机经常面临的高温高应变率耦合环境作为实验条件,在5种温度下开展了CoCrFeNiMn多主元合金的动态压缩实验和变形后试样的塑性变形机理微观表征。结果表明:在1273 K的高温环境中,多主元合金的动态屈服强度可达200 MPa,表现出较好的耐高温性能;随着动态塑性应变的增加,材料内部出现了晶粒粗化的现象,并且在晶界处具有更高的亚结构孕育能力。此外,量化了不同环境温度下动态塑性变形过程中绝热温升的变化规律,指出了现有动态本构关系对CoCrFeNiMn多主元合金在宽温度域内动态应力-应变关系预测能力的不足。最后,通过解耦分析初始屈服与塑性流动阶段的温度效应,建立了一个指数形式的唯象动态本构方程。该本构方程可用于预测冲击载荷作用下宽温度域内多主元合金的屈服强度和塑性流动规律。

纯钽薄壁构件高速级进拉深应变率效应及成形性研究

针对纯钽薄壁构件高速拉深成形过程中因应变率效应引起的成形性问题,首先开展纯钽薄板拉伸应变率效应研究及相关本构模型参数识别,构建考虑材料应变率效应的高速拉深成形Johnson-Cook本构模型,结果表明,纯钽薄板表现出明显的应变率强化效应,动态加载下的屈服强度远高于准静态拉伸下的屈服强度。然后开展钽电容器外壳高速级进拉深成形热力耦合仿真及成形实验研究,分析构件在低速和高速级进拉深成形时的壁厚、温度场分布情况,结果表明,壁厚分布仿真结果与实验结果较为相符,成形速度增大时会导致最终成形件壁厚非均匀性增加;最终级进拉深成形件的最大减薄区出现在筒壁靠中间区域,该区域温度最高且其温度与成形速度正相关;不同速度下的最终成形筒形件的金相组织没有发生明显变化,仅不同变形区的晶粒形状和大小略有差异。

高应变率荷载作用下钢筋与ECC的黏结滑移关系研究

采用水泥基复合材料(engineering cementitious composite,ECC)替代混凝土可以提高结构在偶然荷载作用下的抗连续倒塌性能,但在悬链线大变形阶段钢筋与ECC间可能会出现黏结滑移破坏。基于分离式霍普金森压杆(SHPB)试验装置,进行了钢筋与ECC的动态黏结滑移性能试验,分析了ECC强度等级、应变率、钢筋直径对极限黏结强度、刚度和滑移量的影响规律,获得了高应变率下钢筋与ECC的平均黏结滑移曲线,得到其黏结滑移破坏模式。并与静态黏结滑移试验进行对比,得到了动态黏结强度增强因子。进一步,通过钢筋开槽内贴应变片法,获得不同锚固位置的黏结应力及相对滑移的分布规律,提出黏结位置函数。最后,根据试验结果得到钢筋与ECC平均黏结滑移本构,进而乘以黏结位置函数得到考虑锚固位置影响的动态黏结滑移本构,为ECC结构构件设计及有限元分析提供试验依据和理论参考。

S500MC钢本构模型及其在吸能结构中的应用

首先对S500MC钢进行准静态拉伸和动态冲击试验,获得不同应变率下材料应力-应变关系;其次分别采用J-C本构模型、修正J-C本构模型和C-S本构模型描述S500MC钢的动态力学性能,基于试验结果标定了本构模型参数,并对3种模型准确性进行了验证;最后基于薄壁结构吸能过程仿真,研究J-C模型和C-S模型对结构吸能响应的影响。结果表明:S500MC钢具有明显的应变率强化效应,修正J-C本构模型和C-S本构模型均能较好描述其动态力学特性,在不同冲击速度下,考虑应变率效应时,结构比吸能提高1.46%~9.95%,平均压溃力增加5.36%~11.04%。