Failure loads of spot welds under combined opening and shear static loading conditions

Failure loads of spot welds are investigated under combined opening and shear static loading conditions. Square-cup specimens were used to obtain the failure loads of mild steel spot welds under a range of combined opening and shear loads. Optical micrographs of the cross-sections of spot welds before and after failure were examined to understand the failure processes under different combinations of loads. The experimental results indicate that under nearly pure opening loads, shear failure occurs in the heat affected zone along the nugget circumferential boundary. Under combined opening and shear loading conditions, necking/shear failure starts near the nugget in the stretching side of the base metal sheet. According to the experimental observations, a simple lower bound limit load analysis is conducted. The results of the lower bound limit load analysis quantitatively agree with those of the experiments. A simple closed-form equation is proposed to characterize the failure loads of spot welds under combined opening and shear static loading conditions. The failure load is expressed as a function of the tensile strength of the base metal, the nugget size, the sheet thickness, the loading angle for characterization of combined loads, and an empirical coefficient for the given welding schedule.     

Failure loads of spot weld specimens under impact opening and shear loading conditions

Failure loads of spot weld specimens are investigated under impact combined loading conditions. A set of test fixtures was designed and used to obtain failure loads of mild steel spot weld specimens under combined opening and shear loading conditions. Three different impact speeds were applied to examine the effects of separation speed on failure loads. Micrographs of the cross-sections of failed spot welds were obtained to understand the failure processes in mild steel specimens under different impact combined loads. The experimental results indicate that the failure mechanisms of spot welds are very similar for mild steel specimens at various impact speeds. These micrographs show that the sheet thickness can affect the failure mechanisms. For 1.0 mm specimens, the failure occurs near the base metal in a necking/shear failure mode. For 1.5 mm specimens, the failure occurs near the heat-affected zone in a shear failure mode. Based on the experimental results, the effects of the inertia force, the separation speed, and the loading angle on the failure loads of spot welds are investigated. Failure criteria are proposed to characterize the failure loads of spot welds under impact combined opening and shear loads for engineering applications. The failure load can be expressed as a function of the tensile strength of the base metal, the nugget size, the sheet thickness, the maximum separation speed, the loading angle, and empirical coefficients for a given welding schedule.     

Failure of spot welds under in-plane static loading

Under in-plane loading conditions, two independent modes contribute to the failure of a spot weld: the in-plane shear mode and the in-plane rotational mode. In this work, the failures of both modes under large static load are examined individually. To study the combined failure of these two modes, two special test coupons are designed. The first coupon contains one spot weld. The second coupon contains five spot welds. Tests conducted in this work show that a very simple force-based failure criterion can be used to predict the failure of a spot weld under large in-plane combined static loads. Current multiaxial failure theory cannot explain this combined failure. This force-based spot weld failure criterion fits current automotive industry needs for body shell finite element application very well.     

A force-based failure criterion for spot weld design

This paper suggests a very simple, force-based formula that combines four failure modes into one dimensionless equation to govern spot weld failure under general static loading conditions. The four failure modes are shear, rotation, normal and peel. The normal separation mode and the peel mode are corresponding to mode I (opening mode). The tensile/shear mode is mode II (sliding mode), and the in-plane rotation mode is mode III (tearing mode). Test coupons and test fixtures are designed and tested to establish and verify this equation. To further verify this equation, a long difficult to understand automotive spot weld failure problem was studied. Applying finite element-calculated resultant loads to the proposed formula resulted in analytical values that correlated very well with the long time field observed spot weld failures. This analytical prediction reasonably explained the spot weld failure mechanism and provided good design directions to improve the durability of the auto structure.     

Failure criterion for reinforced concrete beams and plates subjected to membrane force,bending and shear

In this paper, a failure criterion for reinforced concrete plates is derived through the kinematic method in the framework of the limit analysis theory. This criterion is expressed in terms of the stress resultant variables: membrane force, shear force and bending moment at once. The aim of the authors is to be able to predict the failure of reinforced concrete plate structures in statics or in slow dynamics using directly the internal forces (membrane and shear forces and moment) resulting from a finite-element computation.In a first step, a beam criterion is derived. The closed form expression of the criterion shows that it is made up of two parts, one independent of the moment (i.e. depending only on the normal force and the shear force) and one depending on the normal force, the shear force and the bending moment. This structure of the criterion allows to determine two failure modes: shear failure and bending failure.Then in a second step, the beam criterion is extended to the case of reinforced concrete plates. The obtained criterion is partly numerical and partly a close form expression. It gives an upper bound of the load, and when this limit load is reached, the criterion is able to supply, on one hand, the failure mode (as seen in the beam case) and, on the other hand, the angles of the failure plane in the reinforced concrete plate section.Thirdly, the criterion is implemented in the finite element software Europlexus and validated with respect to punching experimental tests. We show that the criterion must be used with an effectiveness factor applied on the concrete compressive strength.     

Full Field Strain Measurement of Resistant Spot Welds Using 3D Image Correlation Systems

This paper describes local strain measurements of electrical resistance spot welds for three sheet stack-ups of Dual Phase (DP600) and Mild steel under quasi-static tensile loading. The experiments were designed to measure local strain distributions at the vicinity of the spot welds using a modified tensile-shear specimen geometry that allows a strain measurement system to access such area. The electrode tip type used was B-nose, and surface indentation levels were 30% and 50% of the sheet thickness. Local strains at critical locations in resistance spot welds were measured using non-contact 3D image correlation systems (ARAMIS) during quasi-static tension tests. The measured local strains were also compared with results offered by a finite element analysis.     

A new approach for failure criterion for sheet metals

The interpretation of sheet forming simulations relies on failure criteria to define the limits of metal deformation. The common requirements for these criteria across a broad range of application areas have not yet been satisfied or fully identified, and a single criterion to satisfy all needs has not been developed. Areas where existing criteria appear to be lacking are in the comprehension of the effects of non-proportional loading, general non-planar and triaxial stress loading, and process and material mechanisms that differentiate between necking and fracture. This study was mainly motivated to provide an efficient method for the analysis of necking and fracture limits for sheet metals. In this paper, a model for the necking limit is combined with a model for the fracture limit in the principal stress space by employing a stress-based forming limit curve (FLC) and the maximum shear stress (MSS) criterion. A new metal failure criterion for in-plane isotropic metals is described, based on and validated by a set of critical experiments. This criterion also takes into consideration of the stress distribution through the thickness of the sheet metal to identify the mode of failure, including localized necking prior to fracture, surface cracking, and through-thickness fracture, with or without a preceding neck. The fracture model is also applied to the openability of a food can for AA 5182. The predicted results show very good agreement with the experimentally observed data.     

Geometric functions of stress intensity factor solutions for spot welds in lap-shear specimens

In this paper, the stress intensity factor solutions for spot welds in lap-shear specimens are investigated by finite element analyses. Three-dimensional finite element models are developed for lap-shear specimens to obtain accurate stress intensity factor solutions. In contrast to the existing investigations of the stress intensity factor solutions based on the finite element analyses, various ratios of the sheet thickness, the half specimen width, the overlap length, and the specimen length to the nugget radius are considered in this investigation. The computational results confirm the functional dependence on the nugget radius and sheet thickness of the stress intensity factor solutions of [Zhang, S., 1997. Stress intensities at spot welds. International Journal of Fracture 88, 167–185; Zhang, S., 1999. Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding Journal 78, 173s–179s]. The computational results provide some geometric functions in terms of the normalized specimen width, the normalized overlap length, and the normalized specimen length to the stress intensity factor solutions of [Zhang, S., 1997. Stress intensities at spot welds. International Journal of Fracture 88, 167–185; Zhang, S., 1999. Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding Journal 78, 173s–179s] for lap-shear specimens. The computational results also indicate that when the spacing between spot welds decreases, the mode I stress intensity factor solution at the critical locations increases and the mode mixture of the stress intensity factors changes consequently. Finally, based on the analytical and computational results, the dimensions of lap-shear specimens and the corresponding approximate stress intensity factor solutions are suggested.     

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．     

A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions

A combined necking and shear localization analysis is adopted to model the failures of two aluminum sheets, AA5754 and AA6111, under biaxial stretching conditions. The approach is based on the assumption that the reduction of thickness or the necking mode is modeled by a plane stress formulation and the final failure mode of shear localization is modeled by a generalized plane strain formulation. The sheet material is modeled by an elastic-viscoplastic constitutive relation that accounts for the potential surface curvature, material plastic anisotropy, material rate sensitivity, and the softening due to the nucleation, growth, and coalescence of microvoids. Specifically, the necking/shear failure of the aluminum sheets is modeled under uniaxial tension, plane strain tension and equal biaxial tension. The results based on the mechanics model presented in this paper are in agreement with those based on the forming limit diagrams (FLDs) and tensile tests. When the necking mode is suppressed, the failure strains are also determined under plane strain conditions. These failure strains can be used as guidances for estimation of the surface failure strains on the stretching sides of the aluminum sheets under plane strain bending conditions. The estimated surface failure strains are higher than the failure strains of the forming limit diagrams under plane strain stretching conditions. The results are consistent with experimental observations where the surface failure strains of the aluminum sheets increase significantly on the stretching sides of the sheets under bending conditions. The results also indicate that when a considerable amount of necking is observed for a sheet metal under stretching conditions, the surface failure strains on the stretching sides of the sheet metal under bending conditions can be significantly higher.     

A criterion for the onset of void coalescence under combined tension and shear

Depending on the relative positions of voids and on the loading conditions, shear loading components can play an important role in the void coalescence process leading to ductile fracture. Yet, most void coalescence criteria including the original criterion of Thomason, and its various extensions/improvements, take only normal loads into account and neglect the contribution from shear loads to coalescence. Shear can affect both the stress/strain at the onset of coalescence and the direction of deformation localization. In this paper, first, the predictive capabilities of different coalescence criteria without shear effect are critically assessed and the expressions involved in the original Thomason criterion are fine-tuned by comparing with 3D finite element calculations performed on a unit cell containing a spheroidal void. Then, the improved Thomason criterion is theoretically extended—by using limit load analysis—to incorporate the effect of shear. The predictions of this new coalescence criterion are in good agreement with the results produced by 3D finite element calculations, for both loadings involving or not a shear component.     

水平圆柱薄壳非轴对称载荷作用内力分析

近年来大直径圆柱形薄壳结构烟风煤粉管道的使用呈增长趋势.水平圆柱薄壳在非轴对称载荷作用下的内力常按整体梁理论或壳的无矩理论计算,无法反映载荷作用边界的弯曲应力.本文结合圆柱壳的无矩理论和弯矩理论,得到了简支水平圆柱薄壳在任意高度内部积灰(粉)、风、雪、自重、地震作用下的内力解析解,且理论解与三维有限元分析结果非常接近.研究结果可推广到类似的非轴对称变形圆柱壳,并为水平薄壁圆柱壳结构设计提供依据.     

Geometric functions of stress intensity factor solutions for spot welds in U-shape specimens

In this paper, the stress intensity factor solutions for spot welds in U-shape specimens are investigated by finite element analyses. Three-dimensional finite element models are developed for U-shape specimens to obtain accurate stress intensity factor solutions. In contrast to the existing investigations of the stress intensity factor solutions based on the finite element analyses, various ratios of the sheet thickness, half specimen width, half specimen length, and corner radius to the nugget radius are considered in this investigation. The computational results confirm the functional dependence on the nugget radius and sheet thickness of Zhang’s analytical solutions. The computational results provide a geometric function in terms of the normalized half specimen width, normalized half specimen length, and normalized corner radius to Zhang’s analytical solutions. The computational results also provide a geometric function in terms of the aspect ratio of the specimen to complete Lin and Pan’s analytical solution. Finally, based on the analytical and computational results, the dimensions of U-shape specimens are suggested.     

Quasi-static crush behavior of aluminum honeycomb specimens under non-proportional compression-dominant combined loads

The quasi-static crush behavior of aluminum 5052-H38 honeycomb specimens under non-proportional compression-dominant combined loads is investigated by experiments. A test fixture was designed such that dominant compressive and shear loads with respect to the strongest material symmetry direction can be controlled and applied independently. Compression-dominant combined loads and pure compressive loads were applied in different sequences to induce non-proportional combined loads. The experimental results show that the normal crush and shear strengths in combined loading regions and the normal crush strengths in pure compressive loading regions of the non-proportional combined loads are quite consistent with the existing phenomenological yield criterion based on the experimental normal crush and shear strengths under proportional combined loads. The experimental results also indicate that the sequence of loading paths for the non-proportional combined loads does not affect the crush strengths when compared with those obtained under proportional combined loads. In addition, the experimental results indicate that the non-normality plastic flow behavior of honeycomb specimens under non-proportional combined loads is consistent with that under proportional combined loads. Finally, specimens crushed under non-proportional combined loads show developments of different stacking patterns of folds in different loading regions of the non-proportional combined loads. The experimental results suggest that the incremental stress–strain relation for the transition loading path within the so-called yield surface from one yield state to another may be related to the displacement increments that correspond to the change of microscopic folding mechanisms instead of the usual elastic relation according to the classical plasticity theory.     

考虑内力分项贡献度的框架构件重要性评价

提出了一种水平和竖向荷载共同作用下的框架结构构件重要性评价方法。首先,基于线弹性材料假设,利用应变能方程和节点-外荷载关系计算梁柱构件的轴力、剪力和弯矩;然后,定义构件内力分项计算值与抗力分项值之比为构件分项重要性系数,用于体现构件抗力利用水平;再组合各内力分项系数,针对不同外荷载形式定义构件综合重要性系数,用于体现构件对框架体系整体承载力的贡献;最后,通过两榀框架算例验证了方法的可行性,可为框架的结构优化设计和连续性倒塌分析提供定量依据。     

含腐蚀缺陷的管道静力性能试验测试研究

为研究腐蚀缺陷对管道承载力的影响,本文分别进行了含腐蚀缺陷管道在轴压载荷、弯曲载荷以及轴压和弯曲复合载荷作用下的静力失效过程测试。通过不同载荷作用下管道的荷载-位移曲线以及荷载-应变曲线来分析管道的失效模式和失效机理;通过有限元分析结果与试验测试结果验证其准确性。结果表明:腐蚀缺陷使管道在三种不同荷载作用下的极限承载力均有所下降;针对文中所研究的管道及其腐蚀缺陷,在轴压载荷作用下管道承载力下降了18.4%,在弯曲载荷作用下管道承载力下降了20.96%,在轴压和弯曲复合载荷作用下管道承载力下降了13.3%;管道中腐蚀缺陷位置的管壁厚度减小,该位置应变发展迅速,首先进入塑性屈服状态,最终导致该腐蚀位置发生弹塑性屈曲失效。     

板片空间结构初始缺陷的动力稳定性影响分析

对板片空间结构体系的研究大都局限于静力载荷工况，结构在动力载荷作用下的稳定性及失效特征研究仍相对缺乏．板片空间钢结构先天存在各样缺陷，而缺陷对结构稳定性的影响不可忽略．本文引入拉丁超立方法，结合Budiansky-Roth 准则，提出适用于求解含初始缺陷结构动力临界荷载的方法，对板片空间结构初始缺陷的动力稳定性开展研究．研究表明，相比于其它抽样方法，拉丁超立方法能显著减少样本数，有效提高计算效率．针对典型的板片空间结构，施加不同方向的阶跃荷载，分析了节点位置偏差缺陷、杆件截面尺寸缺陷以及板片厚度缺陷对板片空间结构临界承载力的影响．结果显示，节点位置偏差缺陷对该结构临界承载力影响最为显著，其它两类缺陷影响甚微．     

Mechanics of advancing pin-loaded contacts with friction

This paper considers finite friction contact problems involving an elastic pin and an infinite elastic plate with a circular hole. Using a suitable class of Green's functions, the singular integral equations governing a very general class of conforming contact problems are formulated. In particular, remote plate stresses, pin loads, moments and distributed loading of the pin by conservative body forces are considered. Numerical solutions are presented for different partial slip load cases. In monotonic loading, the dependence of the tractions on the coefficient of friction is strongest when the contact is highly conforming. For less conforming contacts, the tractions are insensitive to an increase in the value of the friction coefficient above a certain threshold. The contact size and peak pressure in monotonic loading are only weakly dependent on the pin load distribution, with center loads leading to slightly higher peak pressure and lower peak shear than distributed loads. In contrast to half-plane cylinder fretting contacts, fretting behavior is quite different depending on whether or not the pin is allowed to rotate freely. If pin rotation is disallowed, the fretting tractions resemble half-plane fretting tractions in the weakly conforming regime but the contact resists sliding in the strongly conforming regime. If pin rotation is allowed, the shear traction behavior resembles planar rolling contacts in that one slip zone is dominant and the peak shear occurs at its edge. In this case, the effects of material dissimilarity in the strongly conforming regime are only secondary and the contact never goes into sliding. Fretting tractions in the forward and reversed load states show shape asymmetry, which persists with continued load cycling. Finally, the governing integro-differential equation for full sliding is derived; in the limiting case of no friction, the same equation governs contacts with center loading and uniform body force loading, resulting in identical pressures when their resultants are equal.     

堆载下单桩负摩阻力工作性状非线性数值分析

利用三维非线性数值方法对一算例在堆载作用下桩侧负摩阻力进行了计算分析。计算结果揭示了摩擦型、端承型桩负摩阻力工作性状的异同; 分析了堆载速度、桩顶荷载对负摩阻力的影响: 堆载越快,负摩阻力越小; 在无桩顶荷载作用下,由负摩阻力引起的下拉荷载最大,可视为常规方法设计的上限值; 桩顶荷载与堆载施工顺序对负摩阻力的影响也很大,先施加桩顶荷载,后进行堆载所产生的负摩阻力最大,反之最小。