Fatigue crack propagation of through cracks in thin sheets under combined traction and bending stresses

ABSTRACT Fatigue crack propagation tests of through cracks in 3 mm thick aluminium alloy 6013‐T6 plates, under combined membrane and bending stresses were carried out. Five different values for the ratio of bending to membrane stresses, SB, were examined: 0, 0.55, 1.25, 1.8 and 2.23. Firstly, the results were elaborated by taking into account only the membrane stress and the front dimension of the crack for the evaluation of the stress intensity factor range. The results relevant to the lower SB values, evaluated in this mode, show good agreement with the results obtained when only the membrane stress was applied, while the results obtained at the higher SB values exhibit a remarkable increase in the crack propagation rate. The results were successively evaluated on the basis of tabular stress intensity factor solutions available in the literature; the agreement between the predicted and the experimental data occurs when mean values of stress intensity factor, rather than local values, were used at the back face of the plate, i.e., the face where the bending produces a compressive stress, to counteract the high gradient of stress intensity factor present in this area.     

Analysis of multiple cracks in thin coating on orthotropic substrate under mechanical and residual stresses

The analysis addresses a typical failure development pattern in thin films consisting of a system of multiple surface cracks leading to and branching along or near the interface between the film and the base material. The process is driven by thermal residual stresses and/or mechanical loading. Due to the high temperature gradients during the fabrication process, usually a net of surface cracks develops, which gives the appearance of a granular structure of the surface. A periodic array of parallel surface cracks is assumed. A “unit cell” or single cracked segment attached to the substrate is analyzed instead by assuming the channel cracks are spaced more or less uniformly and perfectly aligned in parallel in the transverse direction of the coating. The analysis is specialized to orthotropic and transversally isotropic materials. The problem is solved using FEM combined with the reciprocal theorem. Matched asymptotic procedure [Leguillon D, Sanchez-Palencia E. Computation of singular solutions in elliptic problems and elasticity. Paris: Masson; 1987; Vu-Quoc L, Tran VX. Singularity analysis and fracture energy-release rate for composites: piecewise homogenous-anisotropic materials. Comput Methods Appl Mech Engng 2006;195:5162-97] is used to derive the change of potential energy. Higher-order terms in the asymptotics are considered. The competition between penetration and debond for periodically distributed edge cracks especially near the critical value of the ratio of fracture spacing to the layer thickness is examined.     

Buckling under combined loading of thin,flat-walled structures by a complex finite strip method

A finite strip method is presented for determining the initial buckling stresses of any structure consisting of a series of thin flat isotropic plates rigidly connected together at their longitudinal edges. Each plate may be subjected to a combination of longitudinal and transverse compression, longitudinal in-plane bending, and shear, and it is assumed that the buckling mode, of whatever type, is sinusoidal in the longitudinal direction. Due to the presence of shear, the perturbation forces and displacements which occur at the edges of component plates during buckling are out of phase, and this is accounted for by defining their magnitudes in terms of complex quantities. Stiffness matrices relating the amplitudes of these forces and displacements are derived using an approximate method based upon assumed displacement functions across the width of the plate. It is shown how the method can be used to calculate natural frequencies of prismatic structures, and finally an indication of the accuracy of the method is given together with some illustrative results.     

基于传递矩阵的钻孔应变法测量薄板残余应力

针对ASTME837标准中钻孔应变法测量薄板工件残余应力计算精度低、计算过程复杂的现状,引入弹性力学应变传递矩阵,根据应力叠加原理推导出残余应力与测量应变关系的解析表达式,进而实验研究采用应变传递矩阵计算残余应力的精度.结果表明:与标定值相比,采用传递矩阵计算的残余应力相对误差绝对值均值小于2％,采用ASTM E837...     

不锈钢母材及其焊缝金属材料单拉本构关系研究

对12个奥氏体型及12个双相型不锈钢正面角焊缝和侧面角焊缝连接试件进行了单调拉伸试验,考察了不同焊接工艺对角焊缝连接力学性能的影响。结果表明：采用氩弧焊焊接工艺的不锈钢角焊缝试件破坏面与电弧焊焊接工艺的试件破坏面形状相差较大,后者破坏面更加光滑;同时由于受到复杂应力的作用,正面角焊缝试件的真实破坏角度并不为相关规范规定的理论值45°;对于奥氏体型不锈钢角焊缝,氩弧焊试件与电弧焊试件的强度比分别为1.03 (正面角焊缝试件)及1.13 (侧面角焊缝试件),相对变形量之比为1.46及1.11;而对于双相型不锈钢角焊缝,两者的强度比分别为1.12和1.04,相对变形量之比为1.66及1.45;氩弧焊试件表现出了更好的力学性能。对于两种不锈钢材料,正面角焊缝强度均远大于侧面角焊缝的强度,建议在工程设计和相关规范的编制/修订中考虑正面角焊缝强度提高的影响。     

Effects of plasticity on residual stresses measurement by hole drilling method

Since the fundamental relationships of hole drilling method are derived based on elastic behavior of materials (ASTM E837), there are some limits in determination of high residual stresses (higher than half of yield stress). These limits due to the plastic deformations around the hole were caused by high stresses and their concentrations. In this study the effects of plasticity and mechanical behavior of materials on measured residual stresses were investigated. The results show that the errors of measurements are considerable when the behavior of materials is close to elastic-perfectly plastic. Magnitude and direction of high residual stresses also have some effects on the results. We defined weighted mean stress and used in conjunction with effective stress. The results in different cases show that using this method with proper correction coefficients significantly decreased the errors.     

Measurement of residual stresses in CFRP laminates by X-ray diffraction method

The fabrication of CFRP laminates from prepregs involves curing at elevated temperatures. Residual stresses are set up due to the difference in thermal expansion coefficient between the matrix and the fibre. In this investigation, the X-ray diffraction method is used to measure the curing stresses in CFRP laminates by incorporating a very fine layer of aluminium particles during the lay up of the laminate. A calibration procedure is followed to correlate the strain in the crystalline particles, as measured by X-rays, with the composite strain and stress. Curing stresses measured by this technique are quite close to the value calculated from the differential coefficient of thermal expansion.     

Prediction of fracture instability in thin sheets by finite element method

A fracture instability study has been made for narrow thin panels with central cracks. The quasi-static energy approach in conjunction with finite element method has been employed for the prediction of critical crack length corresponding to a given applied stress level. The corresponding plane-stress fracture toughness, K_Ic has been shown to differ considerably with regard to that obtained from tests following the standard practice. However, the plane stress fracture toughness value obtained experimentally based on the predicted critical crack length is found to be in close agreement with the theoretically obtained value.     

Measurement of residual stresses in thick composite cylinders by the radial-cut-cylinder-bending method

Thick fabric composite cylinders for nozzle parts in solid rocket motors should be designed to endure the extreme temperature and pressure of combustion gas. As the thickness of the composite cylinder increases, fabricational residual stresses due to the anisotropic thermal expansion or shrinkage of fabric composites also increase, which induces inter-laminar failures. Therefore, the accurate estimation of the residual stresses is indispensable for the development of thick fabric composite cylinders.

In this paper, the residual stresses in thick cylinders made of carbon fabric phenolic composites were measured by a new radial-cut-cylinder-bending method. To obtain the residual stresses from the measured relative strains during the radial-cut operation, a bending test of the cylinder with the radial-cut was performed instead of measuring the material properties with respect to radial positions. The thermal residual stresses were also calculated by finite element method considering shear deformation of fabric layers, and compared with the measured residual stresses by the new method, from which it was found that the new simple method estimated the residual stresses pretty well. Also the inter-laminar tensile strength at the position of maximum radial residual stress could be obtained from the bending test.     

Determination of residual shear stresses in composites by a modified layer-removal method

The layer-removal method is often used for measurement of internal stresses in homogeneous polymeric materials. In order to extend the use of the method to laminated composites containing shear stresses, certain refinements are needed. These include (i) determination of twisting moments, (ii) use of varying material properties (elastic moduli) through the thickness of the composite plate, (iii) use of geometric non-linear analysis accounting for large deformations, and (iv) measurement not only of normal curvatures but also twisting curvatures and normal and shear strains. These refinements are necessary, because a non-symmetric laminate is created when layers are removed, which shows large (twisting) curvatures. The modified layer-removal method was theoretically validated on a typical compression-moulded continuous fibre laminate (polyetherimide/glass) and a typical injection-moulded short fibre-reinforced laminate (polycarbonate/glass). The modified method produced good results and the need to use the modified layer-removal analysis is clearly demonstrated. © 1998 Chapman & Hall     

Experimental method for determining through thickness residual hoop stresses in thin walled pipes and tubes without inside access

The determination of through thickness residual stresses in pipes and pressure vessels is of growing interest because of emphasis placed on life prediction, design, and failure analysis of piping systems. Most of the through thickness residual stress measurement techniques require the placement of gauges on the outside and inside of the pipe. These methods are severely hampered when gauges cannot be placed on the inside of the pipe. This constraint could arise for small diameter pipes, long pipes or for pipes that have been used in a service condition causing corrosion or fouling of the inner surface.
This paper focuses on the first step of a three step procedure for determining residual hoop stresses in thin walled pipes and tubes. The method described is designed for cases where it is impossible to place gauges on the inside of the pipe. The method yses biaxial strain gauges on the outside of the pipe and involves a through thickness axial cut of the pipe. Based on the change in strain on the outside of the pipe, changes in the hoop residual stress distribution due to the axial cut are obtained with the method presented here. The method provides a means to evaluate changes in stresses on both the outside surface and the inside surface of the pipe as well as an evaluation of the change in through thickness hoop stress distribution at any location in the pipe cross section. This paper further demonstrates that the problem of shortening long pipes to enable placement of gauges on the inside of the pipe can result in the loss of significant residual stress information.     

Effect of residual stresses on fatigue strength of high strength steel sheets with punched holes

The effect of residual stresses on the reverse bending fatigue strength of steel sheets with punched holes was studied for steels with tensile strength grades of 540 MPa and 780 MPa. Tensile and compressive residual stresses were induced around the punched holes. Heat treatment of the specimens with punched holes at 873 K for 1 h decreased the residual stresses around the holes and improved the fatigue strength of the sheets. This result means that the tensile residual stresses induced in the sidewalls of the holes and near the hole edges by punching reduced fatigue strength. The effect of the residual stresses on the fatigue limits of the edges was estimated by the modified Goodman relation using the residual stresses after cyclic loading and the ultimate tensile strength at the fatigue crack initiation sites.