On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part II. Numerical study

Non-linear finite element analyses of quasi-static and high-rate tensile tests with smooth and notched axisymmetric specimens of the structural steel Weldox 460 E have been carried out. The constitutive relation and fracture criterion of Johnson and Cook, which were adopted in the simulations, have previously been determined for Weldox 460 E steel. First, a validation study was completed to assess the accuracy of the constitutive relation and fracture criterion. The numerical results were compared with experimental data from tensile tests under quasi-static and dynamic loading conditions. Secondly, the use of Bridgman's analysis in the identification of the fracture criterion was evaluated, and the influence of adiabatic heating and inertia on the stress triaxiality in the tensile specimens was investigated. The results were finally used to discuss the identification of fracture criteria based on tensile tests with smooth and notched axisymmetric specimens.     

Fracture in single crystal NiTi

This paper presents an investigation of the pseudoelastic transformation of two crystallographic orientations of a single crystal NiTi shape memory alloy (SMA). Both uniaxial tension and notched tension samples are considered with the tensile axes along the [1 0 0] and [1 1 1] directions. The phase transformation is observed using optical techniques in situ. For the uniaxial tension samples, martensite plates and Lüders-band structures are observed. For the notched samples, transformation structures in the [1 0 0] sample appeared predominantly on the sides of the notch and crack tip with stable crack propagation. In the [1 1 1] notched samples transformation occurs directly ahead of the notch and unstable crack propagation is observed. An available work criterion is used to predict the location of the transformation, with good agreement to the experimental observations. The different fracture behavior of the two notched sample orientations is explained utilizing the available work calculations.     

Fracture of composite laminates containing cracks due to shear loading

The responses of graphite/epoxy [0/90/±45] _s , [±45]_2s , [0/90]_2s and [0/±45]_2s composite laminates with and without center cracks were studied under shear loading using the three-rail shear test. The shear stress/strain relationship, the failure mechanisms and the notched strength were analyzed. Substantial amounts of local buckling were observed in some of the laminates. The present paper shows that shear modulus can be determined accurately using the three-rail shear test with proper interpretation of data. Using the minimum strength model, only one characteristic length was needed to predict accurately the notched strength of a composite laminate under shear and tensile loadings.Paper was presented at the 1987 SEM Spring Conference on Experimental Mechanics held in Houston, TX on June 14–19.     

Constitutive model for a semi-crystalline polymer under dynamic loading

This paper deals with a viscoelastic–viscoplastic model for semi-crystalline polymers in crash applications. A polymer behaviour model is implemented in the commercial PAM CRASH© code thanks to a user material card. Global variables (load, displacement) and local variables (strain) are validated on flat and notched tensile specimens by comparing the numerical responses with data obtained by digital image correlation.     

含切口损伤复合材料层合板拉伸失效行为研究

对含有不同切口损伤的复合材料层合板试件进行了拉伸试验,采用电阻应变计同步测量切口损伤前缘区域随载荷的变化,测定含切口损伤层合板的剩余强度,并讨论了损伤长度和损伤角度对剩余强度的影响规律。建立含切口损伤复合材料层合板有限元模型,分析了含切口损伤复合材料层合板的拉伸失效行为,计算了含切口损伤复合材料层合板的剩余强度,确定了剩余强度与切口损伤状态的关系。计算结果与试验结果具有较好的一致性。     

Dynamic strain aging and related instabilities: experimental,theoretical and numerical aspects

Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.     

An analysis of ductile rupture in notched bars

Ductile fracture in axisymmetric and plane strain notched tensile specimens is analyzed numerically, based on a set of elastic-plastic constitutive relations that account for the nucleation and growth of microvoids. Final material failure by void coalescence is incorporated into the constitutive model via the dependence of the yield function on the void volume fraction. In the analyses the material has no voids initially; but as the voids nucleate and grow, the resultant dilatancy and pressure sensitivity of the macroscopic plastic flow influence the solution significantly. Considering both a blunt notch geometry and a sharp notch geometry in the computations permits a study of the relative roles of high strain and high triaxiality on failure. Comparison is made with published experimental results for notched tensile specimens of high-strength steels. All axisymmetric specimens analyzed fail at the center of the notched section, whereas failure initiation at the surface is found in plane strain specimens with sharp notches, in agreement with the experiments. The results for different specimens are used to investigate the circumstances under which fracture initiation can be represented by a single failure locus in a plot of stress triaxiality vs effective plastic strain.     

Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces

In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears.     

应力三轴度的有限元计算修正

对某高强度钢制成的光滑圆棒和缺口圆棒进行了系列准静态拉伸实验,采用ABAQUS对每个试 件进行了数值模拟,得到了该材料的真实应力应变曲线,拟合出了J-C本构模型和失效模型的部分材料常数。 最后,对该高强度钢制成的平板进行了撞击实验,并用得到的J-C模型对平板撞击实验进行了数值模拟,计算 结果与实验结果吻合很好,证明利用数值模拟并修正应力三轴度的方法是可行的。     

16MnR钢缺口试样解理断裂行为研究

研究了低合金热轧钢16MnR缺口试样在$-196\,{^\circ}$C和$-130\,{^\circ}$C的解理断裂机 理. 拉伸试验、单、双缺口四点弯曲实验、断口形貌观察以及有限元分析结果表明, 缺口试 样发生解理断裂时均起裂于夹杂物粒子, 一种位于缺口根部前端(IC型), 另一种位于距缺口 根部较远的条形裂纹前端(SIC型); 且随温度升高, 起裂源的类型从$-196\,{^\circ}$C下的IC 型转变为$-130\,{^\circ}$C下的SIC型. 微裂纹均形核于夹杂物, 最终的断裂由铁素体晶粒尺 寸的微裂纹扩展控制. 缺口试样IC型解理断裂遵循裂纹形核条 件$\varepsilon_{\rm p} \ge \varepsilon_{\rm pc}$和裂纹扩展条件$\sigma_{yy} \ge \sigma_{f}$, 而SIC型解理断裂条件则演化为$\varepsilon_{\rm p}+\varepsilon_{\rm ps} \ge \varepsilon_{\rm pc}$和$\sigma_{yy} +\sigma_{yy{\rm s}} \ge \sigma_{f}$.     

Detection of lueders' lines by means of brittle coating

Use is made of an improvement of Durelli, Kobayashi and Hofer's method¹ for the detection of Lueders' lines by means of brittle coating. The precision of the method is evaluated by using Fry's etching method in comparison. The propagation of Lueders' lines by increments in notched tensile bars is shown. From a comparison with information contained in literature as regards the propagation of Lueders' lines, it results that the well-known theories of elasticity and plasticity predict the propagation of the Lueders' lines in a qualitatively correct way only in special cases. The technical importance of applying the described brittlecoating method is pointed out.     

A combined phenomenological model for the representation of anisotropic hardening behavior in high strength steel line pipes

Line pipes have anisotropic mechanical properties, such as tensile strength, ductility and toughness. These properties depend on both prestrain during the cold forming process and on the anisotropy of the mother plates. In this study, a phenomenological model combining isotropic and kinematic hardening is developed to represent anisotropic hardening behavior of high strength steel line pipes. The model is adjusted on experiments carried out on smooth and notched axisymmetric bars and plane strain specimens. The model is used to simulate bending tests carried out on large pipes containing a geometric imperfection. Numerical results suggest that prestraining in pipe forming process significantly affects the bending capacity of pipes.     

Micromechanical modelling and simulation of chopped random fiber reinforced polymer composites with progressive debonding damage

The aim of the present paper is to provide a quantitative prediction of the elastic-damage behaviour of randomly oriented fiber polymer composites. A constitutive model based on micromechanical considerations is presented. The nucleation and growth of voids induced by progressive fiber debonding is combined with the constitutive relationship. Failure resulting of excessive damage accumulation is captured by a critical void volume criterion and a vanishing element technique. Experimentally, damage accumulation in random glass fiber–polyester composites was monitored by a videoextensometry technique able to control the local strain rate. Good agreement of model predictions with experimental data is pointed out. The model was implemented into a finite element program and numerical applications on composite structures (a tensile specimen and a plate containing a central hole) are presented to illustrate the capability of the approach. Digital image correlation method was also used to measure the full-field strain in a notched specimen under tensile loading. The simulated results compared favourably with those obtained from experiments.     

割口单向叠层板的拉伸应力集中与强度

基于剪滞理论,建立一种分层剪滞模型,分析了含割口的单向叠层板在拉伸载荷作用下的应力重新分布问题,获得了割口前缘完整纤维的应力集中因子.在此基础上,采用细观统计破坏理论,研究了割口单向叠层板的拉伸破坏强度,得到了与现有实验较吻合的结果.     

High temperature sensitivity of notched AISI 304L stainless steel tests

Experiments were designed to determine the failure characteristics of AISI 304L stainless steel under different stress triaxialities and temperatures up to 70% of melt. The data show that as temperature increases the displacement to failure of notched tensile specimens increases. The complex interaction of deformation mechanisms, such as twinning and dynamic recrystallization, appears to negate the damage accumulation at higher temperatures. Microstructural analyses and finite element simulations indicate that voids nucleate, grow, and coalesce more rapidly as temperature and triaxiality increase. Finite element simulations were performed to analyze temperature dependence on the Cocks–Ashby void growth model. The finite element simulations qualitatively show a double-knee that was observed in the notched experimental specimens after loading. The combined experimental–numerical study indicates that failure can be defined at several points in the notch tests when: (1) macrovoids starts to form, (2) the load drop-off occurs, and (3) total perforation of the specimen occurs. These three points occur simultaneously in ambient conditions but occur at different displacements at higher temperatures.     

Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces

The cohesive surface methodology is used in a numerical study of fracture of concrete. The traction vs. separation response is governed by an isotropic damage law in which damage evolves according to a prescribed one-dimensional linear or exponential softening law. Cohesive surfaces are immersed in the continuum to allow for a maximum freedom of crack path selection. The single edge notched four point shear beam and the double edge notched tensile bar are used to study: (i) the influence of the tangential cohesive response on the development of the fracture path and (ii) the mesh alignment sensitivity. It is shown that in the present formulation, the tangential cohesive response has a minor influence on both crack path and global characteristics. Mesh alignment does have a significant influence on the outcome of the numerical analysis.     

Notched tensile strength for long- and short-fiber reinforced polyamide

The point stress criterion and the average stress criterion are applied for evaluating the notched tensile strength of injection-moulded plates with machined and moulded-in notches. Use is made of a characteristic length which is found to be geometry and material dependent.     

Dynamic Necking of Notched Tensile Bars: An Experimental Study

The mechanics of necking inception in dynamically-stretched notched specimens have been investigated. For that task, a systematic experimental campaign of quasi-static and dynamic tensile tests on martensitic steel specimens has been conducted. Samples with and without notches have been considered. Unlike the quasi-static tests, the dynamically-tested notched samples revealed that, under certain loading conditions, flow localization may develop away from the groove. The experimental results presented in this investigation show that the presence of sharp geometrical imperfections in ductile materials subjected to dynamic loading does not necessarily dictate the necking and fracture locus.     

Benefits of Low Modulus of Elasticity and of Fibre Reinforcement of Cement Based Mortars as Thin Bonded Overlay Materials

The paper, associating experiment and simulation approaches, deals with the debonding propagation between a thin bonded cement-based overlay and a substrate simulating a repair of old concrete structure. The material used for the overlay is a fibre reinforced and rubberised mortar. In the experimental investigations, three point static bending tests were carried out on composite specimens. The effects of shrinkage of the overlay, restrained by the substrate, and the role of fibre reinforcement are thus involved. Direct tensile tests on notched specimens were firstly conducted to obtain the tensile strength and the residual normal stress-crack opening relationship. The debonding opening-residual normal tensile stress relationship was investigated by static tensile tests. The propagation of the debonding interface was monitored using a video-microscope with an enlargement of 175x. On the basis of the parameters identified and quantified, the above mentioned static tests were modelled by the finite element method using CAST3M code developed in France by CEA (Commission for Atomic Energy). The model predictions showed good agreement with the experimental results. The shrinkage effect on the durability of the composite specimens was clarified. The results also proved the important role of fibre-reinforcement in restraining the crack opening by transferring stresses through the crack.