Redistribution of residual stresses in a cylindrical piecewise homogeneous shell with crack

We propose a nondestructive theoretical-experimental method for the evaluation of residual welding stresses in piecewise-homogenous cylindrical elements of shell structures based on the solution of inverse problems with the use of the available experimental data. For a structure weakened by a longitudinal crack, the problem of redistribution of stresses near the crack is reduced to a system of singular integral equations whose solution is constructed by the method of mechanical quadratures. As an example, we solve the problem for a piecewise homogeneous cylindrical shell welded from two semiinfinite shells. The dependences of the force and moment intensity factors on the distribution of residual stresses are investigated. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 5, pp. 39–45, September–October, 1999.     

Evolution of residual stresses with fatigue crack growth in integral structures with crack retarders

Bonded straps are investigated for their ability to retard a growing fatigue crack in metallic structures. The evolution of the residual stresses in the vicinity of the strap with fatigue crack growth has been studied. Cracks were grown in single edge-notched tension (SEN(T)) specimens reinforced with either a titanium or a carbon fibre reinforced plastics (CFRP) strap. The residual stress evolution has been measured in situ during crack growth using neutron diffraction, and modelled with a finite element approach. The peak residual stresses induced by the mismatch of the coefficient of thermal expansion between the strap and plate materials were seen to be fairly constant with crack growth. Good correlation between the experimental and the modelling results was found, except at very long crack lengths for a specimen that exhibited considerable fracture surface roughness at long crack lengths. The difference was attributed to wedging of the fracture surface changing the expected stress state, rather than any effect of the strap.     

Influence of residual stresses on stable crack growth

Abstract

The influence of residual stresses resulting from thermal shock and pressure loading on the initiation and stable growth of cracks in pressure vessels and pipes is considered and preliminary calculations have been made. The residual stresses of a precracked vessel of a 0·22Cr–0·75Ni–0·7Mo–Cr steel at an arbitrarily chosen temperature transient have been analysed using the finite element method. After reheating to normal operating temperature, the influence of the remaining residual stresses on the initiation of the assumed crack is considered. The results provide the initial conditions for stable crack growth analysis based on the J–integral method, which is implemented into the non–linear finite element program ADINA.

MST/27     

Effect of residual stresses on ductile crack growth resistance

It is well known that residual stresses influence the ductile fracture behaviour. In this paper, a numerical study was performed to assess the effect of residual stresses on ductile crack growth resistance of a typical pipeline steel. A modified boundary layer model was employed for the analysis under plane strain, Mode I loading condition. The residual stress fields were introduced into the finite element model by the eigenstrain method. A sharp crack was embedded in the center of the weld region. The complete Gurson model has been applied to simulate the ductile fracture by microvoid nucleation, growth and coalescence. Results show that tensile residual stresses can significantly reduce the crack growth resistance when the crack growth is small compared with the length scale of the tensile residual stress field. With the crack growth, the effect of residual stresses on the crack growth resistance tends to diminish. The effect of residual stress on ductile crack growth resistance seems independent of the size of geometrically similar welds. When normalized by the weld zone size, the ductile crack growth resistance collapses into one curve, which can be used to assess the structural integrity and evaluate the effect of residual stresses. It has also been found that the effect of residual stresses on crack growth resistance depends on the initial void volume fraction f₀, hardening exponent n and T-stress.     

Fatigue crack growth in a welded rail under the influence of residual stresses

The effect of welding residual stresses on fatigue crack growth in rail welds is studied. Finite element analysis is used to calculate residual stresses in a flash-butt welded rail. The calculated residual stresses are found to be in good agreement with experimentally determined residual stresses in a welded rail. The redistribution of residual stresses in the welded rail is simulated for a straight track, during heavy-haul operation conditions, using a train-track model. Fatigue crack growth of defects in the weld region is studied using fracture mechanics. In the investigation, a number of parameters such as the axle load, crack location, crack size and rail temperature are varied.     

Numerical investigation of through crack behaviour under welding residual stresses

Numerous engineering structures operate under the presence of residual stresses resulting from welding or other manufacturing processes. In the present work, the effect of typical residual stress fields on stress intensity factors and crack propagation angle of cracks developing into the residual stress field under mixed mode loading conditions is studied. For the calculations a numerical methodology based on linear elastic finite element analysis is used. The presented results provide a useful tool for an efficient assessment of the influence of residual stress field on the crack evolution behaviour.     

Effect of welding residual stresses on fatigue crack growth thresholds

Fatigue crack growth thresholds ΔK_th were determined for friction stir welded butt joints made from aluminium alloys AA2024 and AA6013. Plotting the thresholds as a function of load ratio R showed distinctly higher amounts for welded joints as compared to those for parent material at small load ratios, but differences became smaller with increasing load ratio, until thresholds became finally identical for the highest R values. Applying Döker’s concept of two controlling parameters, namely ΔK and K_max [1], and plotting ΔK_th versus K_max, however, revealed that the effective threshold ΔK_th,eff determined at very high R ratios was nearly independent on the alloy and, simultaneously, was identical for parent material and respective welded joints. Thus, differences in threshold behaviour were only caused by the second threshold K_max,th, which was significantly higher for welded joints as compared to parent material. Differences in K_max,th coincided with compressive residual stresses determined by cut-compliance measurements in terms of stress intensity factors K_rs acting at the crack tip. Based on the analytical approach described by Döker [1], only one characteristic K_rs value was needed to calculate all thresholds of welded joints for 0 ⩽ R ⩽ 1 provided a base material master curve is available.     

Experimental evaluation of the electric pulse effect on residual stresses in a Ti-Al-Si-Ag coating

Experimental results and stress-strain state simulation by the finite element method show that a thin oxidation-resistant coating sputtered onto a titanium alloy substrate develops high-level residual stresses. The electric pulse passed through a coated specimen significantly reduces an average level of residual stresses in the coating. __________ Translated from Problemy Prochnosti, No. 3, pp. 47–52, May–June, 2008.     

Effect of residual stresses on crack behaviour in single edge bending specimens

Residual stresses due to manufacturing processes, such as welding, change the load bearing capacity of cracked components. The effects of residual stresses on crack behaviour in single edge bending specimens were investigated using Finite element analyses. Three parameters (J, Q and R) were used to study the crack behaviour. The J‐integral predicts the size scale over which large stresses and strains exist, the constraint parameter Q describes the crack‐tip constraint as a result of geometry, loading mode and crack depth and the constraint parameter R is used to describe the constraint resulting from residual stresses. To carry out a systematic investigation on the effect of residual stresses on the J‐integral and crack‐tip constraints, models under different combinations of residual stresses and external loads with different crack depths were analysed. It has been shown that the crack‐tip constraint R increased by tensile residual stresses around the crack‐tip. On the other hand, the constraint parameter R decreased and tended to zero at high external load levels.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Numerical analysis of the influence of residual stresses on crack closure in rings

The stress intensity factors which result when an axially cracked ring containing residual stresses is subjected to an external load have been calculated using a numerical method. When partial crack closure occurs, it has been taken into account. The computations show that residual stresses can cause both cracking problems in service and scatter in experimental data. The method uses a finite-element procedure that is similar to those used with contact problems to provide the basis for a numerical solution. The procedure can be applied to any geometrical configuration that can be analyzed with the finite-element method.     

Numerical predictions and experimental measurements of residual stresses in fatigue crack growth specimens

Controlling macro residual stress fields in a material while preserving a desired microstructure is often a challenging proposition. Processing techniques which induce or reduce residual stresses often also alter microstructural characteristics of the material through thermo-mechanical processes. A novel mechanical technique able to generate controlled residual stresses was developed. The method is based on a pin compression approach, and was used to produce well-controlled magnitudes and distributions of residual stresses in rectangular coupons and compact tension specimens typically used in fatigue crack growth testing. Residual stresses created through this method were first computationally modeled with finite element analysis, and then experimentally reproduced with various levels of pin compression. The magnitudes and distributions of residual stresses in experimental specimens were independently assessed with fracture mechanics methods and good correspondence was found between residual stresses produced using the pin compression and processing techniques. Fatigue crack growth data generated from specimens with low residual stresses, high residual stresses resulting from processing, and high residual stresses introduced through the new pin compression technique were compared and validated. The developed method is proposed to facilitate the acquisition and analysis of fatigue crack growth data generated in residual stresses, validate residual stress corrective models, and verify fatigue crack growth simulations and life predictions in the presence of residual stresses.     

On the effect of the residual stresses on the crack opening displacement in a cracked sheet

The residual stress and displacement fields caused by localized plastic flow near a mode I crack tip in a sheet under plane stress conditions are investigated. The present study founds on the classical Dugdale scheme of the plastic flow localization. The residual stress field is considered to be induced by reversed plastic flow near the crack tip caused by an unloading. As it is found the residual stresses around the crack compress the crack tip, while the residual tensile stresses in a distant from the crack tip zone occur. It is shown the maximum residual tensile stresses can reach the significant value of the one third of the yield limit. The length of the compressed plastic zone and the residual displacement distributions are obtained. The exact formula for the residual crack opening displacement to estimate the crack closure is found. Then the next loading of the cracked plate is considered. It is shown that the second loading causes the origin of two plastic zones localized near the crack tip and at the point, where the maximum residual tensile stresses are concentrated. Again, according to the Dugdale scheme of the plastic localization, both the plastic flow zones are modelled as narrow stripes on the line extending the crack. To determine three non-dimensional parameters, characterizing the position of the segment-like plastic flow zones, a non-linear system of equations is obtained and analyzed. The exact formula for the crack opening displacement after a loading–unloading cycle is obtained. An asymptotic analysis (as the linear dimension of the distant plastic flow zone compared with the actual crack length is small) is given. It shows that the effect of the distant plastic flow zone appears as some complementary crack closure.     

Evolution of residual stresses with fatigue loading and subsequent crack growth in a welded aluminium alloy middle tension specimen

Neutron diffraction has been used to measure the evolution of the residual stresses in a VPPA welded Al-2024 alloy middle tension (M(T)) specimen with fatigue loading and subsequent crack growth. The measurements were carried out on the diffractometer ENGIN-X, a time-of-flight instrument, at the ISIS Pulsed Neutron Source. Fatigue crack growth was performed in situ and strain measurements averaged through the thickness of the specimen were made along two orthogonal directions as the crack grew, allowing the stresses in the specimen to be calculated assuming plane stress. 2D finite element simulation of the evolution of the initial residual stress field with crack growth, using an elastic model produced predictions that were in reasonable agreement with the experimental results. The results further indicate that some re-distribution of the residual stress field occurred due to the crack tip plasticity associated with the fatigue loading.     

Effect of residual stresses on interface crack growth by void expansion mechanism

Crack growth along an interface between two adjacent elastic–plastic materials in a layered solid is analysed, using special interface elements to represent the fracture process ahead of the crack-tip. These interface elements account for ductile failure by the nucleation and growth of voids to coalescence. In these elements the stress components normal to the interface and the shear stresses are given by equilibrium with the surrounding material, and the stress component tangential to the interface is determined by the requirement of compatibility with the surrounding material in the tangential direction. It is assumed that the layers are sufficiently thick, so that the plastic regions around the crack-tip are much smaller than the thickness of the nearest layers. The analyses focus on the effect of initial residual stresses in the layered material, or on T-stress components induced during loading. The results show that the value of the T-stress component in the softer material adjacent to the interface crack plays the dominant role, such that a negative value of this stress component gives a significant increase of the interface fracture toughness.     

Influence of residual stresses from shot peening on fretting fatigue crack growth

One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental fretting life results from specimens in a Titanium alloy with and without shot peened surfaces were evaluated numerically. The residual stresses were measured at different depths below the fretting scar and compared to the corresponding residual stress profile of an unfretted surface. Thus, the amount of stress relaxation during fretting tests was estimated. Elastic–plastic finite element computations showed that stress relaxation was locally more significant than that captured in the measurements. Three different numerical fatigue crack growth models were compared. The best agreement between experimental and numerical fatigue lives for both peened and unpeened specimens was achieved with a parametric fatigue growth procedure that took into consideration the growth behaviour along the whole front of a semi‐elliptical surface crack. Furthermore, the improved fretting fatigue life from shot peening was explained by slower crack growth rates in the shallow surface layer with compressive residual stresses from shot peening. The successful life analyses hinged on three important issues: an accurate residual stress profile, a sufficiently small start crack and a valid crack growth model.     

Effects of welding residual stresses on fatigue crack growth behaviour in butt welds of a pipeline steel

In the present test the fatigue crack growth rate in the parent plate, weld and cross-bond regions was measured and the results were correlated with the stress intensity range ΔK and the effective stress intensity range ΔK_eff. It is indicated that the welding residual stresses strongly affect the crack growth rate. For the weld metal and cross-bond compact tension specimens in which crack growth is along the weld line the fatigue crack growth rate increases as the crack grows. However, for the T compact tension specimen in which crack growth is perpendicular to the weld line at a constant value of applied ΔK the crack growth rate initially decreases as the crack grows. Particularly, at a low constant value of applied ΔK the crack growth rate obviously decreases and the crack fails to grow after short crack growth. When the crack grows to intersect the welded zone, the fatigue crack growth rate gradually increases as the crack grows further. It is clear that the effect of welding residual stresses on the crack growth rate is related to the position of the crack and its orientation with respect to the weld line. Finally, the models of welding residual stress redistribution in the compact tension specimens with the growing crack and its influence on the fatigue crack closure are discussed. It appears that for a butt-welded joint one of the crack closure mechanisms may be considered by the bend or rotation deformation of crack faces due to the welding residual stress redistribution as the fatigue crack grows in the welded joint.