A method for fatigue analysis of metallic and composite materials under asymmetric high-cycle loading

A new method of plotting limit stress diagrams is set forth. The method is based on the hypothesis of unified limit diagram invariant to the number of cycles to failure. The unified diagram is given by a transcendental power function whose exponent is considered an additional material constant characterizing the sensitivity of the material to cycle asymmetry (stress ratio). The equations derived on the basis of this function encompass all forms of limit stress diagrams, including convex, nearly rectilinear, and concave ones. The method is tested for a wide range of metallic and composite materials subjected to asymmetric tension-compression, bending, and torsion.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 106–116, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels

Abstract

In this article, we investigated the effect of martensite morphology on the mechanical properties and formability of dual phase steels. At first, three heat treatment cycles were subjected to a low-carbon steel to produce ferrite–martensite microstructure with martensite morphology of blocky-shaped, continuous, and fibrous. Tensile tests were then carried out so as to study mechanical properties, particularly the strength and strain hardening behavior of dual phase steels. In order to study the formability of dual phase samples, Forming Limit Diagram was obtained experimentally and numerically. Experimental forming limit diagram was obtained using Nakazima forming test, while Finite Element Method was utilized to numerically predict the forming limit diagram. The results indicated that the dual phase samples with fibrous martensite morphology had the highest tensile properties and strain rate hardening out of the three different microstructures. Blocky-shaped martensite morphology, on the other hand, had the worst mechanical properties. The study of the strain hardening behavior of dual phase sample by Kocks–Mecking-type plots, evinced two stages of strain hardening for all specimens with different microstructures: stages III and IV. The forming limit diagram of dual phase steels also proved that samples with fibrous martensite morphology had the best formability compared to other two microstructures. The simulated forming limit diagram manifested that there is a good agreement between experimental results and those obtained by FEM.     

Fatigue strength of metals and composites under repeated high-cycle torsion

The limiting stresses are determined and constant fatigue life diagrams for high-cycle torsion with repeated stress cycle are plotted using the limiting-state models obtained based on the hypothesis of a unified constant-life diagram, which is invariant to the number of cycles to failure. The unified constant-life diagram is given by a transcendental power function whose exponent is an additional parameter characterizing the sensitivity of the material to the asymmetry of the stress cycle. The calculated results and experimental data for carbon and alloyed steels and composite materials are in good agreement __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 19–28, February 2008.     

考虑拉压强度差效应的厚壁圆筒承载能力分析

应用双剪统一强度理论，考虑材料的拉压异性和同性，推导了在内压力和轴力联合作用下的厚壁圆筒的塑性极限载荷表达式．在该表达式中，当反映中间主应力效应的系数取不同的值时，就能得到按Tresca屈服准则、线性逼近的Mises屈服准则和双剪应力屈服准则的计算结果，并且绘制了在相应准则下的极限应力线图．从而可知：在三维应力状态下，应用该理论，可以获得极限载荷分析的精确解；极限载荷线图与三种屈服准则的屈服曲线是相吻合的；计算的结果可以用于拉压异性和同性的材料，为工程应用提供了理论依据．     

Hill（1979）屈服准则的展开及在金属薄板成形极限图中的应用

本文对于Hill(1979)屈服准则在平面应力条件下进行了展开,给出了五种特定条件下的等效应力和等效应变速率表达式,对这些特例的凸条件检验表明,其中的四种可做为合理的屈服函数,将这些屈服函数应用于金属薄板在拉伸范围内的成形极限图的M—K理论预测,获得了较为理想的结果。     

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.     

用损伤理论方法预测铝合金薄板成型极限

应用各向异性损伤理论研究2024-T3铝合金薄板的成形极限,通过构造有限元单胞模型预测薄板结构的极限应变.单胞模型由两相材料组成:铝合金基体和金属强化物.基体采用全耦合弹塑性-损伤本构方程描述,而金属强化物则视为弹脆性材料.采用所提出的缩颈准则,得到了双轴拉伸状态下铝合金薄板的极限应变,和实验结果比较两者吻合较好.研究结果揭示有限元单胞模型可以提供铝合金的细观损伤机理信息,当忽略材料的损伤影响,采用金属薄板成型理论的研究结果将过高估计薄板的极限应变.     

线性强化材料厚壁圆筒的统一极限分析

运用统一强度理论对承受内压的拉压屈服强度不同的线性强化材料的厚壁圆筒进行了极限载荷分析，得到了适用于多种材料的厚壁圆筒极限载荷的统一解析式．     

考虑材料拉压异性的固支圆板塑性极统一解

本文采用最新的统一强度理论求出了固支圆板的塑性极限荷载,内力场及速度的统一解;得出了强度理论参数b及材料的不同拉压比α对塑性极限的影响曲线,所给出的解可以灵活地适用于各种不同特性的材料及机械、土木、航空等工程的相关结构中,文献中已有的Tresca解,Mises解和双剪统一屈服准则解均为本文的特例,本文的统一解还给出了一系列新的结果,统一解大于Tresca,Mohr-Coulomb的单剪理论解,它可以更好地发挥材料的强度潜力,工程应用可以取得明显的经济效益。     

Forming limit diagram prediction of tailor welded blank by modified M–K model

The Marciniak and Kuczynski (M–K) model for necking prediction in sheet metal forming was based on the in-plane forming. Bending which was resulted from out-of-plane forming was not considered in the M–K model. Whereas most of the sheet metal forming processes and also standard test of hemispherical punch for forming limit diagram are out-of-plane forming, it is important to consider bending effect in the M–K model. Therefore, in this study bending strain is added to stretching strain of M–K model and a new model is presented for forming limit diagram (FLD) prediction. This modified M–K (MM–K) model is written in the python programming language and it is used as a post-processing criterion for FLD prediction in the commercial software Abaqus. The MM–K model was used to predict FLD and weld line movement in the tailor welded blank forming. It was found that the predicted results by MM–K model are in a good agreement with experimental data.     

不同拉压特性的厚壁圆筒极限内压统一解

厚壁圆筒在实际工程领域中应用广泛,若能精确计算出极限内压,对预防事故发生,降低风险有重要意义.工程中存在许多材料,其拉压强度和拉压模量均存在差异,这些差异对极限内压的大小有显著影响.以往研究表明,仅考虑拉压强度与拉压模量的一个方面,计算结果与实际情况存在一定的误差.本文基于双剪统一强度理论,综合考虑中间主应力效应及材料拉压强度和拉压模量的不同,推导了内压作用下厚壁圆筒的弹、塑性状态的应力分布及弹性极限内压、塑性极限内压与安定极限内压的统一解,通过与其他文献对比分析验证了本文计算结果的正确性,分析了半径比、统一强度理论参数、拉压强度比与拉压模量系数对弹性极限内压、塑性极限内压及安定极限内压的影响.结果表明:统一解均随半径比和统一强度理论参数的增大而增大,随拉压强度比的增大而减小,弹性极限内压随材料拉压模量系数的增大而减小,当壁厚增加到一定值后,安定极限内压随材料拉压模量系数的增大而减小;材料的拉压模量不同、拉压强度差异对厚壁圆筒的安定性影响显著,考虑中间主应力效应可使材料的潜能得到更充分发挥,极限内压随半径比的变化规律可为选择合理壁厚提供参考,该结论可为厚壁圆筒的工程应用提供理论依据.     

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基于27种合金钢与铝合金的机械、力学性能，分析对比了3种理论估算疲劳极限方法的估 算结果，发现3种方法中只有两种方法能够比较精确地估算材料的疲劳极限; 当引 入强度系数和应变硬化指数与常规机械与力学性能的关系之后，这两种方法都可借助材料的 常规机械与力学性能估算疲劳极限，估算过程中的限制性条件``高强度钢'应予取消.     

Methodology to assess integrity with application to collector copper lamellas

The performance of engineering components and structures is strongly influenced by the interaction between design, manufacture and materials. A methodology to assess the integrity of a circular collector is presented by investigating the failure of copper lamellas. The investigated circular collector, having 315 copper lamellas, is one of the main parts of an electric motor. The fracture of the copper lamellas was observed in normal operation. This unexpected fracture required an investigation of the fracture origin, in order to improve the initial design. The numerical results of the finite element analysis on the stress field in the copper lamellas for the operating regimes, and the stress concentration effects are shown. Failure assessment diagram, based on notch stress intensity factor, was considered in order to estimate if crack initiation can occur. Finally a study of crack propagation will present comparatively the numerical obtained crack path against the one observed in-service.     

Fatigue strength of metallic and composite materials under repeated tension-compression

The fatigue strength of metallic and composite materials under combined static and cyclic loading is analyzed. The analysis is based on limit-state models, which allow us to describe limiting-stress diagrams of all known shapes, including convex, rectilinear, S-shaped, and concave. The fatigue strength of the following materials is evaluated: carbon and alloy steels, aluminum alloys, creep-resistant nickel alloys, unidirectional composites, plastic laminates, glassfiber-reinforced plastics, and polymers. The calculated results and experimental data are in satisfactory agreement __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 48–58, January 2006.     

Generalised forming limit diagrams showing increased forming limits with non-planar stress states

The forming limit diagram and its associated analytical and experimental techniques has been widely used for 40 years with the assumption that sheet deformation occurs inplane-stress. Some hydro-forming type processes induce significant normal stress across the workpiece and this has led to a small number of extended formability analyses. However, recent work on the incremental sheet forming process which is known to give higher formability than conventional sheet pressing has shown that the repeated passage of a tool over the sheet leads to significant through-thickness shear strains being induced in the workpiece. Accordingly this paper explores the forming limits of sheet forming processes which induce any possible proportional loading, including all six components of the symmetric stress tensor. Marciniak and Kuczyinski’s famous (1967) analysis is extended to allow such loading, and a new generalised forming limit diagram (GFLD) is proposed to allow visual representation of the resulting forming limit strains. The GFLD demonstrates that forming limits can be increased significantly by both normal compressive stress and through-thickness shear. This increased formability is confirmed by experiments on a specially designed ‘linear paddle testing’ apparatus in which a conventional uniaxial test is augmented by the action of a paddle that ‘strokes’ the sample while also applying a normal force. Tests on the rig show that the paddle action leads to enhanced engineering strains at failure up to 300%. The insight gained in this paper is significant for process analysts, as it may explain existing discrepancies between prediction and experience of forming limits, and is important for designers who may be able to use it to expand process operating windows.     

Predicting the strain hardening characteristics of ageing alloys under combined loading

The paper examines the effect of the initial structure and prestrain on the yield stress of a number of ageing steels and alloys under combined loading in the cases of like and opposite directions of preloading and reloading. The parameters of yield loci are calculated for the case of combined two-axial tension. Their predicted dependence on temperature, ageing time, and prestrain is experimentally checked. As they increase, strain hardening changes from isotropic to kinematic and then to mixed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 116–125, June 2007.     

简支圆板在复杂荷载作用下的塑性极限荷载统一解析解

本文采用双剪统一屈服准则对受线性荷载和边缘弯矩联合作用下的简支圆板进行了塑性极限分析，考虑了联合作用的两种形式，分别给出了统一的解析解。得到了极限荷载随不同屈服准则的变化曲线。对于不同的材料，本文均能给出相应的极限荷载。已有的Tresca准则、Von Mises准则、双剪应力准则的解答是文中解答的特例或逼近。本文得到的一系列有规则变化的解析解，可以适用于各种拉压强度相同材料的简支圆板的塑性极限荷载求解。文中统一解大于Tresca单剪理论解，它可以更好地发挥材料的强度潜力，工程应用可以取得明显的经济效益。     

用双剪统一屈服准则求解某些问题的塑性极限荷载

本文采用俞茂宏统一屈服准则对固支圆板、矩形板进行了塑性极限荷载分析,得出了相应的统一解形式。选择不同的参数b,可以得出不同工程材料的塑性极限荷载,具有较好的普遍性和适用性。文献中已有的解均为本文的特例。     

The shear fracture of dual-phase steel

Unexpected fractures at high-curvature die radii in sheet forming operations limit the adoption of advanced high strength steels (AHSS) that otherwise offer remarkable combinations of high strength and tensile ductility. Identified as “shear fractures” or “shear failures,” these often show little sign of through-thickness localization and are not predicted by standard industrial simulations and forming limit diagrams. To understand the origins of shear failure and improve its prediction, a new displacement-controlled draw-bending test was developed, carried out, and simulated using a coupled thermo-mechanical finite element model. The model incorporates 3D solid elements and a novel constitutive law taking into account the effects of strain, strain rate, and temperature on flow stress. The simulation results were compared with companion draw-bend tests for three grades of dual-phase (DP) steel over a range of process conditions. Shear failures were accurately predicted without resorting to damage mechanics, but less satisfactorily for DP 980 steel. Deformation-induced heating has a dominant effect on the occurrence of shear failure in these alloys because of the large energy dissipated and the sensitivity of strain hardening to temperature increases of the order of 75 °C. Isothermal simulations greatly overestimated the formability and the critical bending ratio for shear failures, thus accounting for the dominant effect leading to the inability of current industrial methods to predict forming performance accurately. Use of shell elements (similar to industrial practice) contributes to the prediction error, and fracture (as opposed to strain localization) contributes for higher-strength alloys, particularly for transverse direction tests. The results illustrate the pitfall of using low-rate, isothermal, small-curvature forming limit measurements and simulations to predict the failure of high-rate, quasi-adiabatic, large-curvature industrial forming operations of AHSS.