Limit load in bending of welded samples with a soft welded joint

The limit load is one of the basic characteristics in estimating the workability of various structures, in particular, welded structures with a soft welded joint. In some cases, the difference in the yield stresses of the base material and the welded joint material is so pronounced that plastic strains are localized in a thin welded joint. The upper bound of the limit load of a welded sample subjected to bending under conditions of plane strains is obtained with allowance for certain specific features of such a distribution of strains. A comparison with the known solution is performed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 216–222, March–April, 2008.     

考虑塑性和刚度不匹配的焊接残余应力估算

现有残余应力计算方法未能考虑材料塑性变形和焊接接头刚度不匹配的影响,使得焊接残余应力计算结果和实际残余应力存在较大偏差.在2219-T87铝合金钨极氩弧焊焊接头残余应力测试基础上,提出一种基于非线性有限元和材料弹性模量分区的残余应力—释放应变曲线的残余应力计算方法,研究了材料塑性变形和接头刚度不匹配对焊接残余应力计算的影响.结果表明,焊接接头中非均质材料塑性不匹配可以引起对于残余应力计算的较大误差;材料塑性变形对残余应力的影响大于接头刚度不匹配对残余应力的影响.所提出方法修正了传统方法在焊接接头的残余应力计算中由于未考虑接头非均质材料塑性不匹配而引起的误差.     

Influence of plastic anisotropy on predictions of some engineering approaches in fracture mechanics

We study the influence of plastic anisotropy on the predictions of some engineering models of fracture mechanics. We consider a welded specimen with a crack in the weld joint under tensile loads. The weld jointmaterial and the mainmaterial are assumed to obey the orthotropic yield condition. A comparison with the isotropic cases shows that the limit load significantly depends on the plastic anisotropy parameters of thematerials. Since this load is one of the basic input parameters of engineering models of fracture mechanics, the plastic anisotropy parameters must strongly affect the predictions of such models, and these should be taken into account in the structural analysis.     

Stress distribution in L-shaped butt joint: Welded or bonded

The stresses in L-shaped butt joint, welded or bonded, are obtained by the finite element method. Correction for kinematic nonlinearity is made by including an upward movement of the joint. The local stress field behavior depends on the bead dimension, applied load and the governing material properties. The ways with which these parameters affect the joint behavior are investigated by comparing results obtained from a linear and nonlinear analysis.     

Variational methods for the steady state response of elastic–plastic solids subjected to cyclic loads

Solids (or structures) of elastic–plastic internal variable material models and subjected to cyclic loads are considered. A minimum net resistant power theorem, direct consequence of the classical maximum intrinsic dissipation theorem of plasticity theory, is envisioned which describes the material behavior by determining the plastic flow mechanism (if any) corresponding to a given stress/hardening state. A maximum principle is provided which characterizes the optimal initial stress/hardening state of a cyclically loaded structure as the one such that the plastic strain and kinematic internal variable increments produced over a cycle are kinematically admissible. A steady cycle minimum principle, integrated form of the aforementioned minimum net resistant power theorem, is provided, which characterizes the structure’s steady state response (steady cycle) and proves to be an extension to the present context of known principles of perfect plasticity. The optimality equations of this minimum principle are studied and two particular cases are considered: (i) loads not exceeding the shakedown limit (so recovering known results of shakedown theory) and (ii) specimen under uniform cyclic stress (or strain). Criteria to assess the structure’s ratchet limit loads are given. These, together with some insensitivity features of the structure’s alternating plasticity state, provide the basis to the ratchet limit load analysis problem, for which solution procedures are discussed.     

Mathematical programming approaches for the safety assessment of semirigid elastoplastic frames

This paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads. The inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces. As is necessary for this class of structures, geometric nonlinearity is taken into account. Moreover, only a 2nd-order geometric approximation is included as this is sufficiently accurate for practical structures. The work described has a twofold contribution. First, we develop an algorithm that can robustly and efficiently process the complete (path-dependent) nonholonomic response of the structure in a stepwise (path-independent) holonomic fashion. The governing formulation is cast in mixed static-kinematic variables and leads naturally to what is known in the mathematical programming literature as a mixed complementarity problem (MCP). The novelty of the proposed algorithm is that it processes the MCP directly without using some iterative (and often cumbersome) predictor–corrector procedure. Second, in the spirit of simplified analyses, the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility, material and geometric nonlinearities, and limited ductility. Our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Finally, four numerical examples, concerning practical structures and benchmark cases, are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes.     

Size effects on the plastic collapse limit load of thin foils in bending and thin wires in torsion

Following a previous paper by the author [Strain gradient plasticity, strengthening effects and plastic limit analysis, Int. J. Solids Struct. 47 (2010) 100–112], a nonconventional plastic limit analysis for a particular class of micron scale structures as, typically, thin foils in bending and thin wires in torsion, is here addressed. An idealized rigid-perfectly plastic material is considered, which is featured by a strengthening potential degree-one homogeneous function of the effective plastic strain and its spatial gradient. The nonlocal (gradient) nature of the material resides in the inherent strengthening law, whereby the yield strength is related to the effective plastic strain through a second order PDE with associated higher order boundary conditions. The peculiarity of the considered structures stems from their geometry and loading conditions, which dictate the shape of the collapse mechanism and make the higher order boundary conditions on the (microscopically) free boundary be accommodated by means of a boundary singularity mechanism. This consists in the formation of thin boundary layers with unbounded stresses, but bounded stress resultants which —together with the regular bulk stresses— contribute to the value of the collapse load. Closed-form solutions are provided for thin foils in pure bending and thin wires in pure torsion, and in particular the limit bending and torque moments are given as functions of an adimensionalized internal length parameter.     

Numerical study of the plastic behaviour in tension of welds in high strength steels

The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.     

Study of size effects in the Dugdale model through the case of a crack in a semi-infinite plane under anti-plane shear loading

The main objective of this work is to prove that, with the Dugdale model, the small size defects, comparatively to the material characteristic length, are practically without influence on the limit load of structures. For that, we treat the case of a crack in a semi-infinite plane under anti-plane shear loading. Using integral transforms, the elasticity equations are converted analytically into a singular integral equation. The singular integral equation is solved numerically using Chebychev polynomials. Special care is needed to take into account the presence of jump discontinuities in the loading distribution along the crack lips.      

A phenomenological model for anisotropic creep in a multipass weld metal

Creep strength of welded joints can be estimated by continuum damage mechanics. In this case constitutive equations are required for different constituents of the welded joint: the weld metal, the heat-affected zone, and the parent material. The objective of this paper is to model the anisotropic creep behavior in a weld metal produced by multipass welding. To explain the origins of anisotropic creep, a mechanical model for a binary structure composed of fine-grained and coarse-grained constituents with different creep properties is introduced. The results illustrate the basic features of the stress redistribution and damage growth in the constituents of the weld metal and agree qualitatively with experimental observations. The structural analysis of a welded joint requires a model of creep for the weld metal under multiaxial stress states. For this purpose the engineering creep theory based on the creep potential hypothesis, the flow rule, and assumption of transverse isotropy is applied. The outcome is a coordinate-free equation for secondary creep formulated in terms of the Norton–Bailey–Odqvist creep potential and three invariants of the stress tensor. The material constants are identified according to the experimental data presented in the literature.     

Strain gradient plasticity,strengthening effects and plastic limit analysis

Within the framework of isotropic strain gradient plasticity, a rate-independent constitutive model exhibiting size dependent hardening is formulated and discussed with particular concern to its strengthening behavior. The latter is modelled as a (fictitious) isotropic hardening featured by a potential which is a positively degree-one homogeneous function of the effective plastic strain and its gradient. This potential leads to a strengthening law in which the strengthening stress, i.e. the increase of the plastically undeformed material initial yield stress, is related to the effective plastic strain through a second order PDE and related higher order boundary conditions. The plasticity flow laws, with the role there played by the strengthening stress, are addressed and shown to admit a maximum dissipation principle. For an idealized elastic perfectly plastic material with strengthening effects, the plastic collapse load problem of a micro/nano scale structure is addressed and its basic features under the light of classical plastic limit analysis are pointed out. It is found that the conceptual framework of classical limit analysis, including the notion of rigid-plastic behavior, remains valid. The lower bound and upper bound theorems of classical limit analysis are extended to strengthening materials. A static-type maximum principle and a kinematic-type minimum principle, consequences of the lower and upper bound theorems, respectively, are each independently shown to solve the collapse load problem. These principles coincide with their respective classical counterparts in the case of simple material. Comparisons with existing theories are provided. An application of this nonclassical plastic limit analysis to a simple shear model is also presented, in which the plastic collapse load is shown to increase with the decreasing sample size (Hall–Petch size effects).     

Fatigue strength of welded joints based on local, semi-local and nominal approaches

Analysis based on the so-called “local approach” is made to estimate the fatigue strength of welded joints. Numerical analyses or strain gauges are employed for finding the stress and/or strain state in the vicinity of the weld toe. The notch stress intensity factor (NSIF) approach applied to fillet welded joints, as far as the opening angle between the weld and the main plate surface is constant (e.g. 135°, typical for many fillet welds), is able to rationalise the fatigue strength data both for different joint geometries and absolute dimensions. The NSIF approach has been previously developed as an extension of the Linear Elastic Fracture Mechanics (LEFM) to open V-notches and is based on the exponential local stress field around the V-notch tip. Several different “local approaches”, although simpler and more practical than the NSIF, are based on the stress (or strain) values determined beyond the exponential local one. To distinguish such approaches from the NSIF based one, we define the former as semi-local or nominal approaches while the latter is a local approach. The paper underlines that the local approaches, differently from the other ones, are able to unify in a single scatter band the fatigue strength data obtained from welded joints having different geometry and absolute dimensions.     

A New Multiaxial Specimen for Determining the Dynamic Properties of Adhesive Joints

Adhesive joints are increasingly employed for bonding critical parts of industrial structures. Therefore, adhesive joints become a key element in design, and their mechanical characterization is of the utmost importance. Significant advancement has been realized for their characterization under quasi-static loadings; however characterization techniques are rather limited for dynamic loadings. Indeed, due to the complex paths of waves through structures, existing dynamic characterization techniques will not characterize only the adhesive joint, but instead will characterize the complete assembly containing the joint and the adherents. Moreover, multiaxiality control of the loading on the adhesive joint is difficult to achieve. This paper proposes an innovative experimental technique for the characterization of adhesive joints under dynamic multiaxial loadings. The experimental method relies on three main components: i) a conventional split Hopkinson pressure bar (SHPB) apparatus, ii) a novel specimen, denoted as DODECA, which enables testing of three distinct multiaxial loadings using the same method and iii) local strain and stress measurements performed by digital image correlation (DIC). The paper describes all steps of the experimental procedure, including the underlying preparation of the specimen and the measuring methods. The stress and strain in the adhesive joint are estimated directly from the experimental data both during loading and at the failure point. Finally, the dynamic material behavior of the adhesive joint is identified from the data.     

Slip Damping Mechanism in Welded Structures Using Response Surface Methodology

Response surface methodology (RSM) is a technique used to determine and represent the cause and effect of relationship between true mean responses and input control variables influencing the responses as an n-dimensional hyper surface. Welded joints are used extensively in many modern industries to fabricate jointed structures that contribute significantly to the inherent slip damping. The main problem faced in the manufacture of such structures is the selection of optimum combination of input variables for achieving the required damping. This problem can be solved by developing the mathematical models through effective and strategic planning and executing experiments by RSM. This investigation highlights the use of RSM by designing a four-factor three-level central composite rotatable design matrix with full replication of planning, conducting, executing and developing the mathematical models. This is useful for predicting the mechanism of interfacial slip damping in layered and welded structures. The design utilizes the initial amplitude of excitation, number of tack welded joints and surface roughness at the interfaces as well as the material property to develop a model for the logarithmic damping decrement of layered and welded structures with different end conditions. Experimental results indicate that the proposed mathematical models adequately predict the logarithmic damping decrement within the limits of the factors that are being investigated.     

半潜式钻井平台管道钢构支架极限强度研究

钢构支架是半潜式钻井平台管道支吊架的主要类型之一,钢构支架的极限强度是管道系统正常工作的重要保障。研究结构极限强度的方法有理论分析、有限元数值仿真和实验分析。在分析极限理论的基础上由静力法计算四种钢构支架试件的极限载荷;利用MSC软件对试件极限载荷进行数值仿真分析,并对有限元模型化技术进行讨论;对试件进行实验极限载荷测试,对比分析了三种方法测得的极限载荷。结果表明,三种分析方法计算得到结构的极限载荷基本一致,对于结构形式较为简单的结构通过理论分析可以得到简化解析解析解;数值仿真分析中采用合理的有限元模型化技术(结构有限元模型、边界、约束等)可得到精度较高的计算结果。     

Low-cycle fatigue in welds

Hour-glass-shaped specimens were made from ASTM A-516, grade 55, steel plates which had been welded together. The specimens were manufactured so that the weld material was at the minimum section. The specimens were strain cycled about zero mean strain and the results were compared with tests conducted on specimens taken from the parent material. When the total strain range vs. cycles to failure was plotted on log-log coordinates, the curves for both the welded and parent-material specimens had nearly the same slope; however, the curve for the welded specimens was displaced downward from that of the parent material. Thus, for a given strain range, the parentmaterial specimens had lives approximately six times greater than the welded specimens. Two-level cumulative-damage tests on the welded specimens indicate that using Σn/N=1.0 is reasonably accurate.     

极限下限分析的正交基无单元Galerkin法

基于极限分析的下限定理，建立了用正交基无单元Galerkin法进行理想弹塑性结构极 限分析的整套求解算法．下限分析所需的虚拟弹性应力场可由正交基无单元Galerkin法直接 得到，所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模 拟．这些自平衡应力场基矢量可由弹塑性增量分析中的平衡迭代得到．通过对自平衡应力场 子空间的不断修正，整个问题的求解将化为一系列非线性数学规划子问题，并通过复合形法 进行求解．算例表明该方法有效地克服了维数障碍问题，使计算效率得到了充分的提高，是 切实可行的．     

不均匀性焊接接头弹塑性断裂力学问题的有限元分析

本文对含裂纹焊接接头的简化模型——软夹硬不均匀裂纹体和硬夹软不均匀裂纹体——进行了弹塑性有限元分析,研究了材质力学性能不均匀性对OOD的影响规律.还研究了在静载和疲劳载荷下材质不均匀性对软夹硬不均匀体裂纹扩展行为的影响.     

螺旋焊线管局部噘嘴应力集中分析

螺旋焊缝局部噘嘴问题是复杂的三维问题，至今没有现成的安全评定公式可以利用，也难以获得纯粹的理论解。应“西气东输”工程之需，本文利用现有直焊缝理论基础，建立了该问题的力学模型，获得了应力集中因子的显式解，给制订螺旋焊线管几保缺陷的安全评定标准提供了理论基础。利用商用有限元工具ABAQUS对螺旋焊线局部噘嘴进行的系统分析显示，本文提供的理论解具有很强的预测能力。     

Prediction of failure in weldments — Part II: Joint with initial notch and crack

This investigation is concerned with predicting failure initiation sites ina butt weld joint under bending. The nonuniform load transmission characteristics through the weld metal, heat-affected zone and base material resulting from alteration in their microstructure are reflected through the macroscopic yield strength parameter. Elastic-plastic stress and strain redistribution is obtained for each increment of load increase. Analyzed in detail are the contours of constant strain energy density for determining the local and global stationary values which are assumed to be related to failure and stability of the system. Failure is predicted to initiate in the heat affected zone at the site of maximum of the minimum local strain energy density function. This corresponds to the experimental observation where cracking starts from the side of the butt joint where local stretching is maximum.