RESIDUAL STRESS FIELDS DURING FATIGUE CRACK GROWTH

This study outlines the distinction between (1) residual stresses at an ideal crack tip, undergoing reversed deformation in the absence of crack closure, and (2) additional residual stresses generated due to plasticity induced closure upon fatigue crack growth. Residual stresses resulting from reversed deformation in plane strain were higher compared to the plane stress case, while residual stresses generated behind the crack tip were more significant in plane stress compared to plane strain. The origin of these residual stresses was studied for two specimen geometries over a wide range of loading conditions. We define a new crack tip parameter, S_tt as the applied stress level that corresponds to the development of tensile stresses immediately ahead of crack tips. The S_tt levels were significantly higher for a fatigue crack than for an ideal crack. We attribute the difference in S_tt levels between these two cases to plasticity induced closure. The results demonstrate the importance of the S_tt parameter, since the stresses ahead of crack tips could remain compressive even when the crack surfaces are open. Moreover, the study emphasizes the need, when describing fatigue crack growth, to incorporate both the closure concept and residual stress field ahead of a crack tip.     

Influence of through-thickness crack shape on plasticity induced crack closure

In most of the previous three‐dimensional (3D) numerical studies of plasticity induced crack closure (PICC), ideal shapes have been assumed for the cracks. The aim of present paper is to study the effect of crack shape on PICC. With this objective a 3D numerical model was developed to predict PICC in middle‐tension (MT) specimens with different thicknesses and crack shapes. The radial size of crack tip elements and the stabilization of closure level were studied to ensure the quality of numerical predictions. Simultaneously, an independent numerical model was developed to predict crack shape evolution, stable crack shapes and corresponding K distributions. Crack closure was found to produce a significant tunnelling effect, with maximum values of ΔK and K_max at the surface. The curved crack presented significant plastic deformation near the free surface which has a high impact on the computation time, compared to the straight crack. The modification of ΔK and K_max with crack shape produced a variation of 38% in opening values at the interior positions, but relatively small variations at the surface. Considering the great influence of crack shape on PICC, it is fundamental to model realistic crack shapes.     

Analysis of high temperature fatigue crack growth behavior

High temperature fatigue crack growth has been examined in the light of the new concepts developed by the authors. We observe that the high temperature crack growth behavior can be explained using the two intrinsic parameters ΔK and K_max, without invoking crack closure concepts. The two-parameter requirement implies that two driving forces are required simultaneously to cause fatigue cracks to grow. This results in two thresholds that must be exceeded to initiate the growth. Of the two, the cyclic threshold part is related to the cyclic plasticity, while the static threshold is related to the breaking of the crack tip bonds. It is experimentally observed that the latter is relatively more sensitive to temperature, crack tip environment and slip mode. With increasing test temperature, the cycle-dependent damage process becomes more time-dependent, with the effect that crack growth is dominated by K_max. Thus, in all such fracture processes, whether it is an overload fracture or subcritical crack growth involving stress corrosion, sustained load, creep, fatigue or combinations thereof, K_max (or an equivalent non-linear parameter such as J_max) remains as one essential driving force contributing to the final material separation. Under fatigue conditions, cyclic amplitude ΔK (or an equivalent non-linear parameter like ΔJ) becomes the second necessary driving force needed to induce the characteristic cyclic damage for crack growth. Cyclic damage then reduces the role of K_max required for crack growth at the expense of ΔK.     

Reflections on identifying the real ΔKeffective in the threshold region and beyond

The use of the crack tip stress intensity factor, K, has survived almost 50 years as the key parameter correlating fatigue crack growth. As time past the range of the stress intensity, ΔK, was recognized as causing alternating plasticity at the crack tip. The threshold level for ΔK was discovered. Further, the occurrence of crack closure was noted which affected the ΔK for different load ratios, R of cyclic loading. The ASTM method of counting the linear part of the load displacement for determining ΔK_open was found to understate the ΔK_effective, which correlates data for different load ratios. One approach to adjust for this problem is the “Partial Closure Model”, where the closure only occurs away from the crack tip. Here it will be discussed that such a model leads to a universal growth law. Moreover, this law shows application in estimating the order of magnitude of crack growth life (<10⁷ cycles) for example with very high cycle fatigue (>10⁹ cycles). Some advances in this application will also be cited.     

EFFECTS OF AIR AND INERT ENVIRONMENTS ON THE NEAR THRESHOLD FATIGUE CRACK GROWTH BEHAVIOR OF ALLOY 718

The near threshold fatigue crack growth behavior of alloy 718 was studied in air and helium environments at room temperature and at 538°C. Tests were performed at 100 Hz and at load ratios of 0.1 and 0.5. At room temperature and at 538°C, the ΔK_th values in helium were lower than in air. The ΔK_th values in air decreased with increasing load ratio. These results can be explained with a model that involves the accumulation of oxide in the crack which enhances crack closure. In the air tests, the oxide build-up on the fatigue fracture surfaces at ΔK_th was of the order of magnitude as the crack tip opening displacement. In the helium tests, no significant build-up of oxide on the fracture surface at threshold was found.     

Analysis of fatigue crack growth behavior of SS 316(N) welds using the unified approach

Fatigue crack growth (FCG) behavior of SS 316(N) weld has been evaluated at different R‐ratios at room temperature and compared with that of the base metal. The FCG resistance of weld is better than that of the base material and is due to the residual stresses developed during the welding. The data were analyzed using the unified approach that considers the two‐parametric (ΔK and K_max) nature of fatigue. The R‐ratio effects in both the base and weld metals are accounted for without invoking the extrinsic parameters, such as plasticity‐induced crack closure. Since the residual stresses are of the monotonic type, they affect the crack growth via the K_max‐parameter. The crack growth trajectory plots were developed, and they show how the two crack tip driving forces, ΔK and K_max, change to overcome the FCG resistance of the weld in relation to that of the base metal. The results also show that the effects from the compressive residual stresses are more dominant at low R‐values and occur via the K_max parameter.     

FATIGUE CRACK GROWTH THROUGH ARALL-4 AT AMBIENT TEMPERATURE

Fatigue cracks were grown in the 5 layer aluminum alloy-Aramid fiber laminate composite ARALL-4 over the range of cyclic stress intensity factors (ΔK) from 3.5 to 91 MPa?m. Near the threshold, crack growth rate was about the same as for unreinforced aluminum alloys, but at high ΔK, crack growth rates were significantly lower. Crack closure was measured over this range of growth rates and found to be different than for unreinforced aluminum alloys. The magnitude of closure was also dependent on crack length. Cracks opened progressively towards the tip with increasing load in much the same way as for unreinforced aluminum alloys. Removal of the aluminum outer layer and some of the epoxy revealed that fibers were intact close to the crack tip, but heavily damaged further away. By adjusting the fatigue crack growth curve of an unreinforced aluminum alloy for the closure exhibited by the composite, it was possible to approximate the crack growth rate for the composite over the lower to mid range of ΔK, but at higher values of ΔK, this model seriously overestimated measured crack growth rates. Therefore, fiber bridging affects both closure and maximum stress intensity factor at the crack tip. Standard fracture mechanics cannot be applied to describe these effects.     

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi‐elliptical surface cracks in a bearing steel was investigated under cyclic shear‐mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear‐mode crack growth in the longitudinal direction of cylindrical specimens. Non‐propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔK_IIth and ΔK_IIIth, were estimated from the shape and dimensions of non‐propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔK_IIth and ΔK_IIIth.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Modellierung des Ermüdungsrisswachstums in Schweißverbindungen unter Berücksichtigung von Schweißeigenspannungen

The present paper contains research results determined within the framework of a project called IBESS (?Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“) by the Materials Mechanics Group of the Technische Universität Darmstadt [1]. Aim is to calculate the fatigue life of welded joints by taking into account the effect of residual stresses and the influence of the weld toe geometry. Here, the fatigue life is regarded as period of short fatigue crack growth. Two and three dimensional finite element models, with cracks as initial defects, are constructed for this purpose. Fatigue crack growth analyses are performed by using the node release technique together with the finite element program ABAQUS. The welding residual stresses as well as the plasticity induced crack closure effects are considered. Structural calculations are performed in order to introduce residual stress fields in finite element models. The calculated compressive residual stress field matches the measured one especially in the weld notch area. The effective cyclic J‐integral (ΔJ_eff) is used as crack tip parameter in a relation similar to the Paris equation for the calculation of the fatigue life. For this purpose, a Python code was written for the determination of ΔJ_eff at every crack length phase. The calculated fatigue lives were compared with experimental data and a good accordance between both results was achieved. The impact of welding residual stresses on ΔJ_eff as well as on the fatigue life during short crack growth was investigated. As expected, results revealed that at lower stress amplitude, a compressive residual stress field is favorable to the fatigue life, whilst a tensile residual stress field is unfavorable. The influence of residual stresses can be neglected only for large load amplitudes.     

FATIGUE CRACK GROWTH AND CLOSURE BEHAVIOUR THROUGH A COMPRESSIVE RESIDUAL STRESS FIELD

Behaviour of fatigue crack growth and closure through a compressive residual stress field is investigated by performing fatigue crack growth tests on welded SEN specimens of a structural steel (JIS SM50A). Depending on the type of the initial residual stress in the region of crack growth, the growth and closure of the crack show different behaviour. In particular, in the transition region from a compressive residual stress field to a tensile residual stress field, the fatigue crack growth rates cannot be described by the effective stress intensity factor range ΔK_eff, based on the measured crack opening stress intensity factor K_op. Also it is found that the R'-method using the data of da/dN vs ΔK for residual stress-free specimens, with the effective stress ratio R'[=(K_max+K_r)/(K_min+K_r)], gives non-conservative predictions of the growth rates in the transition region. Observations of crack closure behaviour in this study indicates that partial opening of the crack occurs and this plays an important role in crack growth through a compressive residual stress field. Based on the concept of a partial opening point (defined and measured in this work), fatigue crack growth behaviour can be better explained.     

A parameter for quantitative analysis of plasticity induced crack closure

Numerical models have been successfully developed to predict plasticity induced crack closure (PICC). However, despite the large research effort a full understanding of the links between physical parameters, residual plastic wake and PICC has not been achieved yet. The plastic extension of material behind crack tip, Δy_p, obtained by the integration of vertical plastic deformation perpendicularly to crack flank, is proposed here to quantify the residual plastic field. The values of Δy_p and PICC were obtained numerically in a M(T) specimen using the finite element method. An excellent correlation was found between PICC and Δy_p which indicates that this parameter controls the phenomenon, and can be used to quantify the effect of physical parameters. An empirical model was developed to predict PICC assuming that the residual plastic field is a set of vertical plastic wedges, that the linear superposition principle applies and that the influence of a particular wedge exponentially decreases with distance to crack tip. The model was applied successfully to predict PICC for different residual plastic fields which provided an additional validation of Δy_p as the parameter controlling PICC.     

Transient behaviour in the numerical analysis of plasticity induced crack closure

A transient behaviour is observed in the numerical analysis of plasticity induced crack closure at the beginning of crack propagation, as the residual plastic field is being formed. The extent of crack propagation prior to plasticity induced crack closure measurement has a major influence on the accuracy of numerical prediction and on computation time. The objective here is to quantify and understand the minimum propagation, Δa_stb, required to obtain stabilized crack opening values. For plane stress state, Δa_stb was found to increase with ΔK. Under plane strain conditions, a peak of closure exists at the beginning of crack propagation for relatively low ΔK values, which promotes relatively large transient periods. Two driving forces explain the stabilization behaviour, the formation of residual plastic wake and the stabilization of plastic strain, but the second seemed to control the phenomenon. Finally, two strategies are proposed to accelerate convergence. The first, consisting of a progressive increase of maximum load, is relevant in plane strain and 3D studies, in order to eliminate the initial peak. The second strategy consists of an extrapolation model and is very effective for plane stress conditions.     

The importance of compressive stresses on fatigue crack propagation rate

This paper is concerned with the importance of compressive stresses on crack propagation rate. In a previous paper, namely ‘Crack Closure Inadequacy at Negative Stress Ratios’, Int. Journal of Fatigue, 26, 2004, pp. 241–252, was demonstrated the inadequacy of the crack closure concept and ΔK_eff, at a negative stress ratio, R=−1, to predict crack propagation rate. It that paper was verified that, at negative stress ratios, crack closure changes with P_max, for the same R ratio. The main conclusion was about plastic properties and mainly cyclic plastic properties, the Bauschinger effect included, on crack propagation when compressive stresses exist. It was then suggested that in the place of the crack closure concept, another concept based on plasticity should be used to explain fatigue crack propagation.In this paper, instead of working with the same negative R ratio (R=−1), a study on the behavior of crack propagation rate as a function of R ratio, from negative to positive stress ratios, is made. Both the effect of P_max and of R ratio is taken into consideration. Measurements of roughness and of crack opening loads are made, in order to verify their influence on crack propagation rate. Different materials, in order to cover different cyclic plastic properties and different sensitivities to roughness are studied (Ck45-cyclic hardening; Ti6Al4V-cyclic softening, and aluminum, Al 7175-cyclically neutral) are studied. Aluminium alloys and titanium alloys are considered to be sensitive to roughness induced crack closure (RICC) while steels are more dependent on plastic properties (PICC).In this study it is emphasized the importance of the compressive part of the cycle, and of cyclic plastic properties, on crack propagation rate. It is reassessed the inadequacy of crack closure concept and ΔK_eff to describe crack propagation rate, at negative stress ratios. It is also verified that models based solely on extrinsic properties of materials, like da/dN−ΔK or da/dN−ΔK (K_max) should also incorporate intrinsic properties of the materials in order to properly correlate fatigue crack growth.     

On R ratio dependence of threshold stress intensity factor range for fatigue crack growth in type 316(N) stainless steel weld

Abstract

The influence of R ratio in the range 0·05–0·4 on the ambient temperature fatigue crack growth behaviour of an austenitic stainless steel weld, SS 316(N), has been studied. Results indicate that the cyclic threshold stress intensity factor ΔK_th increases with decreasing R ratio. The data are compared with those for SS 316, SS 316L and SS 316L(N) base materials from the literature, and various approaches dealing with the R ratio effects are examined. Zhang’s model considering the contribution of the crack tip plasticity to the fundamental fatigue crack propagation process does provide a consistent interpretation for the data.     

Plastic mismatch effect on plasticity induced crack closure: Fatigue crack propagation perpendicularly across a plastically mismatched interface

In the present work, comprehensive investigation of both theoretical analysis and numerical simulation was carried out to investigate the plastic mismatch effect on plasticity induced crack closure (PICC) behavior and effective fatigue crack tip driving force. During the process of crack tip approaching interface, crack tip load and crack tip load ratio will change, resulting in the change of PICC degree. When the crack propagates towards higher strength side, K_op/K_max increases; when the crack propagates towards lower strength side, K_op/K_max decreases firstly and then increases. The two mechanisms of “interface plastic mismatch effect on nominal fatigue crack tip driving force” and “interface plastic mismatch effect on PICC degree” were compared. The second mechanism must be considered when building crack tip driving force model for describing fatigue crack crossing plastically mismatched interface, because it is more physically factual and maybe more important than the first mechanism.     

Derivation of effective stress intensity factors from measured crack face displacements

When a crack is subjected to cyclic shear-mode loading, crack faces interference wedge the crack open and reduce the effective ΔK_II. The methods proposed in the literature to prevent it or to derive the effective ΔK_I and ΔK_II are discussed. It is shown that when crack tip plasticity becomes important it tends to make displacements larger than those predicted by LEFM and to “hide” friction effects. Finite element simulations combining friction and plasticity can separate these two effects, but the analysis of force-sliding displacement loops derived from displacement field measurements based on image correlation is a more straightforward and efficient method.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

A two parameter driving force for fatigue crack growth analysis

A model for fatigue crack growth (FCG) analysis based on the elastic–plastic crack tip stress–strain history was proposed. The fatigue crack growth was predicted by simulating the stress–strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiation in the crack tip region. The model was developed to predict the effect of the mean stress including the influence of the applied compressive stress. A fatigue crack growth expression was derived using both the plane strain and plane stress state assumption. It was found that the FCG was controlled by a two parameter driving force in the form of: . The driving force was derived on the basis of the local stresses and strains at the crack tip using the Smith–Watson–Topper (SWT) fatigue damage parameter: D=σ_maxΔε/2.The effect of the internal (residual) stress induced by the reversed cyclic plasticity was accounted for the subsequent analysis. Experimental fatigue crack growth data sets for two aluminum alloys (7075-T6 and 2024-T351) and one steel alloy (4340) were used for the verification of the model.