Crack Opening Stress Research Articles

In-situ SEM study of fatigue crack growth behaviour in IN718

Fatigue crack growth experiments on Inconel 718 have been performed in a scanning electron microscope at room temperature. The investigated cracks were approximately 1–3 mm long and the samples used were thin 10 mm wide plates. The crack opening stress was found to vary significantly, even in the Paris region, for a constant stress ratio. Crack growth was predominantly found to be either growth on slip planes in a shearing mode, or linking after formation of microcracks ahead of the main crack, which do not require detectable crack opening. A rough crack surface indicates that at room temperature roughness induced crack closure is significant even in the midst of the Paris region, at higher stress intensity factor levels than anticipated. A post experimental examination of the fracture surfaces revealed that a striation forming mechanism was not active at short cracks, but as crack length increased, the occurrence of striations increased in the interior of the specimen. No striations were found in the grains at the specimen surface. As multiple crack growth mechanisms are active, fatigue crack rate predictions need to take all different mechanisms into account to improve accuracy.

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/ W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/ W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J– A 2 three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J– A 2 approach.

Finite element modeling of microstructurally small cracks using single crystal plasticity

Finite element simulations of small fatigue cracks were performed using crystal plasticity theory to describe the deformation behavior near the crack tip. A rate-independent small strain formulation from crystal plasticity theory was implemented. Constant amplitude loads were applied, with a load ratio of R=0.3. Crack opening stresses and crack tip opening displacement ranges were simulated as the crack grew in a single grain, as well as when the crack grew toward a grain boundary. Crack growth in single grains indicated that stabilization of the crack opening stresses occurs relatively rapidly (5–10 μm of crack growth). Studies of crack growth toward a grain boundary revealed that, depending on the orientation of the adjacent grain, the crack growth rate is significantly affected. If the angle of misorientation between the two adjacent grains is small, the neighboring grain can increase the growth rate near the grain boundary. If the misorientation angle is high, the fatigue crack growth rate will be significantly slowed near the grain boundary.

Numerical modelling of plasticity-induced crack closure for interfacial cracks in bi-material specimens

This paper reports the results of a fairly detailed finite element study which modelled the plasticity-induced crack closure (PICC) behaviour of interfacial cracks in various bi-material specimens. In particular, the fatigue crack-opening stress ( S op) level and the crack-tip deformation fields (Modes I and II) have been assessed for a number of different material combinations, chosen so as to throw some light on the effects of modulus of rigidity and strength level of the alloy on PICC. The material combinations included specimens based on aluminium alloy steel, medium strength–high strength steel, and aluminium or steel specimens coated with a rigid ceramic. Results obtained indicate that stabilised values of closure, S op, can be interpreted as supporting the hypothesis that it is the elastic constraint on, and deformability of, the plastic zone surrounding a crack that are the major contributors to PICC, rather than any permanent ‘stretch’ associated with crack growth. Positive Mode II slip of the upper crack face over the lower face (i.e. the upper surface moving over the lower surface towards the crack-tip) can elevate S op level, while a negative slip (i.e. the upper surface moving over the lower surface away from the crack-tip) causes a reduction in its value.

Prediction and correlation of the average crack-opening stress with service load cycles

The crack-opening stresses of a crack emanating from an edge notch in three different materials — a 2024-T351 aluminum alloy, a 1045 annealed steel, and a 1045 quenched and tempered steel specimen — were measured under three different Society of Automotive Engineers (SAE) standard service load histories having different average mean stress levels. In order to capture the actual behavior of the crack-opening stress in the material, the crack-opening stress levels were measured using a 900 x optical video microscope at frequent intervals for each set of histories scaled to two different maximum stress ranges.The crack-opening stress was modeled and the model was implemented in a fatigue notch model and the fatigue lives of notched specimens of the three different materials under the three different spectra scaled to several maximum stress levels were estimated. The average measured crack-opening stresses were within between 6 and 13 percent of the average calculated crack-opening stresses. The fatigue life predictions based on the modeled crack-opening stresses and the fatigue notch model were in good agreement with the experimentally determined fatigue data.In the interest of simplifying the use of crack-opening stress in design, the average crack-opening stress was correlated with the frequency of occurrence of the cycle reducing the crack-opening stress to the average level. The use of a crack-opening stress level corresponding to the cycle causing a reduction to a crack-opening stress reached once per 200 cycles gave a conservative estimate of fatigue life for the soft metals 2024-T351 aluminum alloy and 1045 annealed steel, while for the 1045 quenched and tempered steel the cycle causing a reduction to a crack-opening stress reached once per 10 cycles gave a conservative life estimate.

転位動力学シミュレーションによる疲労き裂進展挙動の検討

The influence of the loading history and stress ratio on the behavior of fatigue crack propagation was investigated through the computer simulation based upon the emission and movement of dislocations from the crack-tip. The result of the simulation showed that there is a power relation between the stress intensity range in the preceding cycles and the threshold value where the crack stops propagating. It was also found that the threshold value obtained by the simulation is closely connected with the stress ratio through the Walker relation. The existence of those relations was explained from the viewpoint that the above two parameters control not only the maximum stress intensity but also the crack opening stress intensity level which is determined by the degree of the shielding effect due to the residual dislocations. This idea was supported by the simulation result that the crack propagation rate was clearly related to the effective stress intensity range which was defined as the difference between the maximum stress intensity and the above crack opening stress intensity.

Influence of Measurement Location on Local Crack Opening Displacement

By means of local measurement with a laser interferometry technique, the difference in fatigue crack opening evaluation results was revealed when the measurements were conducted at different locations along the length of a fatigue crack in an aluminum alloy. It was found that the crack opening stress increases when the measuring location approaches the crack tip. The experimental study leads to a suggestion that the fatigue crack closure result evaluated with the data obtained from a location far from the crack tip will underestimate the closure effect.

832 放射光による超細粒鋼の切欠き近傍の応力分布測定

Stress distribution near a single-edge notch of steel plates with ultrafine-grained surface layers (SUF steels) was measured by monochromatic X-rays from synchrotron radiation. The diffracted X-rays were recorded by an imaging plate. Residual stresses and loading stresses ahead of the notch were determined by the cosα method. When the distance from the notch root was larger than 500mm, the measured stress agreed well with the calculated values. Stress distribution near a fatigue crack was measured by (sin)^2⩛ method. The loading stresses and residual stresses agreed very well with the calculated results. The crack opening stress calculated by the residual stresses also agreed with the experimental result.

Variable amplitude fatigue of spot welds

ABSTRACTA new method for fatigue life prediction of spot welds subjected to variable amplitude loads is proposed. The method is based on the concept of crack closure and is experimentally verified with three different specimens and four different load signals with variable amplitude. Experimental fatigue lives were found to be within a factor of three from the predicted lives. To start with, the stress intensity factor history at the spot weld is calculated with a finite element analysis. Then, crack closure is taken into account: the crack opening stress intensity factor, which is assumed to be constant, is determined from the maximum and minimum in the history. All stress intensities lower than the crack opening level are filtered from the calculated history. The filtered history is then analysed with rain flow count. Finally, fatigue life is predicted with the Palmgren–Miner cumulative damage rule together with an effective (closure‐free) curve for spot welds. In addition, single overload tests were carried out to investigate the assumption of a constant crack opening stress.

Prediction of crack-opening stress levels for 1045 as-received steel under service loading spectra

A crack growth analysis based on a fracture mechanics approach was used to model the fatigue behavior of as-received 1045 steel specimens for three load spectra scaled to various maximum stress range levels. The crack growth analysis was based on an effective strain-based intensity factor, a crack growth rate curve obtained during closure-free loading cycles, and a local notch strain calculation based on Neuber’s rule. The crack-opening stresses were modeled assuming that the crack-opening stress when it is not at the constant amplitude steady-state level for a given stress cycle builds up as an exponential function of the difference between the current crack-opening stress and the steady-state crack-opening stress of the given cycle unless this cycle is below the intrinsic stress range for crack growth or the maximum stress in the cycle is below zero in which cases the crack-opening stress does not change. The crack-opening stress model was implemented in a fatigue notch model and the fatigue lives of the notched annealed 1045 steel specimens under the three different load spectra scaled to several maximum stress levels were estimated. The average measured crack-opening stresses for the various histories and levels were within between 8 and 13% of the average calculated crack-opening stresses. The fatigue life predictions based on the modeled crack-opening stresses were in good agreement with the experimentally obtained fatigue data. The averages of the measured crack-opening stresses and those calculated using the model were nearly the same for all the histories examined. When these average crack-opening stresses were used in the life prediction model they gave predictions as good as those obtained by modeling crack-opening stress on a cycle by cycle basis. The use of a crack-opening stress level corresponding to the cycle causing a reduction to a crack-opening stress reached for 1/200 of the cycles in the history gave a conservative estimate of average crack-opening stress for all the histories.

Finite element modeling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects

Two-dimensional, elastic–perfectly plastic finite element analyses of middle-crack tension (MT) and compact tension (CT) geometries were conducted to study fatigue crack closure and to calculate the crack-opening values under plane-strain and plane-stress conditions. The behaviors of the CT and MT geometries were compared. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus approximately similar initial forward plastic zone sizes. Mesh refinement studies were performed on both geometries with various element types. For the CT geometry, negligible crack-opening loads under plane-strain conditions were observed. In contrast, for the MT specimen, the plane-strain crack-opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for both the CT and MT specimens.

The modified fatigue crack closure concept: further modeling and evaluation

The present study is aimed at evaluating the previously-modified crack closure concept, in which the role of cyclic loading portion below the opening stress intensity factor K.P has been taken into account, by comparison with an earlier developed crack opening stress model as a function of the maximum and minimum cyclic stresses and material-dependent parameters. In this study a geometrical analysis of the load-COD (crack opening displacement) curve is firther developed. Experimental results on 2024-T351 alloy obtained earlier in different laboratories have also verified that the crack opening stress drops when the magnitude of alternating stress cycles exceeds approximately a half of the yield strength. Large stress amplitudes applied to a smooth specimen will cause an instantaneous reduction in the crack opening stress from steady-state levels observed during constant amplitude loading.

Scattering of inhomogeneous wave by viscoelastic interface crack

The reflection, refraction and scattering of inhomogeneous plane waves of SH type by an interface crack between two dissimilar viscoelastic bodies are investigated. The singular integral equation method is used to reduce the scattering problem into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Then, the singular integral equation is solved numerically by Kurtz's piecewise continuous function method. The crack opening displacement and dynamic stress intensity factor characterizing the scattered near-field are estimated for various incident angles, frequencies and relaxation times. The differences on crack opening displacement and stress intensity factor between elastic and viscoelastic interface crack are contrasted. And the effects of incident angle, incident frequency and relaxation time of the viscoelastic material are analyzed and explained by the features of phase lag and energy dissipation of the viscoelastic wave.

Theoretical and numerical aspects of the volumetric approach for fatigue life prediction in notched components

Many macro-mechanical models for fatigue life prediction have been proposed. One of these methods is the ‘volumetric approach’. This paper is a complete investigation in theoretical base, intrinsic features, assumptions and its applicability for various notched components. The macro-mechanical behavior of notch roots and special notch root characteristics in a bi-logarithmic diagram for fatigue crack opening stress corresponding to distance in notch root gives pseudo-fracture mechanics behavior for fatigue cracks in notch roots for specific regions. The effective stress, effective plastic zone and relative stress gradient are determined by means of elastic–plastic finite element analysis. The fatigue failure estimations have very good agreement with the experimental results for various kinds of notch geometry.

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack‐tip slip band model with the plasticity‐induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack‐tip opening displacement range (ΔCTOD), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, ΔCTOD began to decrease. The arrest condition of cracks was given by the threshold value of ΔCTOD. At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.

Simulation of plasticity-induced fatigue crack closure in part-through cracked geometries using finite element analysis

The part-through semi-elliptical surface flaw is commonly encountered in engineering practice. Proper characterization of plasticity-induced crack closure is necessary to predict both flaw growth and flaw shape evolution under cyclic loading. Three-dimensional elastic–plastic finite element analyses are used to model the plasticity-induced closure developed along the surface flaw crack front, and the subsequent crack opening behavior under constant amplitude loading. Resulting crack opening stresses are compared with results from a strip-yield model and with experimentally measured values reported in the literature. It was found that the computed values were larger than those measured.

Fatigue crack growth under variable-amplitude loading: Part I – Model formulation in state-space setting

This two-part paper presents formulation and validation of a non-linear dynamical model of fatigue crack growth in ductile alloys under variable-amplitude loading including single-cycle overloads, irregular sequences, and random loads. The model is formulated in the state-space setting based on the crack closure concept and captures the effects of stress overload and reverse plastic flow. The state variables of the model are crack length and crack opening stress. This paper, which is the first part, presents formulation of the state-space model that can be restructured as an autoregressive moving average (ARMA) model for real-time applications such as health monitoring and life extending control. The second part is the companion paper that is dedicated to model validation with fatigue test data under different types of variable-amplitude and spectrum loading.

Fatigue crack growth under variable-amplitude loading: Part II – Code development and model validation

A state-space model of fatigue crack growth has been formulated based on the crack closure concept in the first part of the two-part paper. The unique feature of this state-space model is that the constitutive equation for crack-opening stress is governed by a low-order non-linear difference equation without the need for storage of a long load history. Therefore, savings in the computation time and memory requirements are significant. This paper, which is the second part, provides information for code development and validates the state-space model with fatigue test data for different types of variable-amplitude and spectrum loading in 7075-T6 and 2024-T3 aluminum alloys, respectively. Predictions of the state-space model are compared with those of the FASTRAN and AFGROW codes.

Evaluation of Fatigue Strength of Cracked Components Based on Analysis of Plasticity-Induced Crack Closure.

The propagation behavior of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. Plasticity-induced crack closure was analyzed for two dimensional through cracks and penny-shaped cracks in plane stress, plane strain and Tresca's yield condition. The plastic constraint factor of penny-shaped cracks in Tresca's yield condition decreases with increasing applied stress. When compared at the same amount of crack extension, the development of crack opening stress with crack extension for through cracks and penny-shaped cracks in plane strain condition was nearly close. The crack opening stress intensity factor at the threshold can be simply approximated as a function of the applied stress and the amount of crack extension. The cyclic resistance-curve method was used to predict the fatigue thresholds of pre-cracked components. When compared at the same initial crack length, the fatigue limit for fracture of penny-shaped cracks in plane strain condition is larger than that of through cracks. On the other hand, the relation between the initial crack length and the fatigue limits for fracture is nearly independent of the defect type.

Application of Hypersingular Integral Equation Method to a Three-Dimensional Crack Terminating at an Interface.

In this paper a three dimensional crack perpendicular to and terminating at a bimaterial interface is considered under general mixed-mode loading. The solution utilizes the body force method and requires Green's functions for perfectly bonded elastic half planes. The formulation leads to a system of hypersingular integral equations whose unknowns are three modes of crack opening displacements. The main-part analytical method is used to investigate the characteristics of stress singularity around the crack front touching the interface. An explicit closed-form expression is given for the singular stress field, which is controlled by general stress intensity factors. The relations between three modes of crack opening displacements and stress intensity factors are also discussed.