Boundary-only element analysis of crack contact under thermal shock

This paper presents a multi-domain boundary integral equation approach of thermally excited crack surface interference observed under thermal transient conditions. According to this model, crack surface displacements and tractions are not free but subject to constraints simulating contact and prevailing overlapping of crack surfaces. The multi-domain approach allows the two faces of a crack to be modeled in independent sub-regions of the body, avoiding singularity difficulties and making it possible to analyze crack closure problems with contact stresses over part of the cracked faces. Crack-tip singularities are modeled through quarter-point elements. In order to approach the interference configuration, the interfacial traction distribution and solve the resulting equations, an iterative numerical procedure is applied. The numerical solution of this non-linear problem yields crack surface displacements and consequently the crack surface interference. Fracture parameters are evaluated from nodal displacements of singular elements utilizing proper formulas. Various results are illustrated and discussed for edge-cracks subjected to steady-state or thermal shock conditions.     

Comparison of virtual crack extension and strain energy density methods applied to contact surface crack growth

The paper is concerned with comparison of two crack propagation methods applied to a two-dimensional computational model of the surface initiated crack growth in the lubricated contact area of meshing gears. The virtual crack extension method and the minimum strain energy density criterion are used for simulation of the crack propagation in the framework of the finite element analysis. The discretised equivalent contact model, with the assumed size and orientation of the initial crack, is subjected to contact loading conditions, accounting for the elasto-hydro-dynamic lubrication effects, tangential loading due to sliding and the influence of lubricating fluid, driven into the crack by hydraulic mechanism. The computational results show that both crack propagation methods give comparable results, although the virtual crack extension method has some clear advantages due to its theoretical superiority in dealing with mixed-mode short crack propagation close to the loading boundary.     

A two-stage model for predicting crack growth due to repeated thermal shock

The growth of cracks in equipment that is exposed to repeated thermal down shocks presents a complex problem of analysis. The transient, highly non-linear nature of the stress profiles that are developed during the shock in addition to localized plasticity and environmental interactions makes difficult any accurate analytical predictions. The use of current analysis techniques based on linear stress approximations can result in overly conservative results that may lead to unnecessary and costly component replacements.This paper outlines results from an experimental investigation into crack growth in notched, flat plate specimens exposed to repeated one-dimensional thermal shocks. Analysis of the results shows that a simple two-stage growth model may be applicable for describing the crack growth. The model is comprised of a high strain fatigue region where crack growth is in the plastic range and a region where growth is described by linear elastic fracture mechanics. Allowances for the effects of mean loads and environment on the crack growth are also included in the model. The model is currently limited to the consideration of carbon steel components, operating at temperatures below the creep range.     

A mixed mode crack growth model taking account of fracture surface contact and friction

Fracture surface interactions, of whatever origin, can significantly affect the stress intensity factor, and consequently, can also be relevant to fatigue crack propagation. In the occurrence of interaction between fracture surfaces, the effective loading cycle experienced by material near the crack tip may be very different from that evaluated on the basis of the external loadings only. The purpose of the work described in this paper is to obtain the effective mode II stress intensity factor, k _IIeff, in a surface cracked elasto-plastic plate with a factory roof fracture surface subjected to an in-plane shear (mode II) loading. A new model estimating the magnitude of the frictional mode II stress intensity factor, k _f, arising from the mismatch of the fracture surface roughness during in-plane shear, is developed. Furthermore, the results of this study are employed in modeling the fatigue response of the surface cracked plates subjected to mixed mode loading.     

An atomistic model of crack extension by kink propagation

A model originally developed to characterize the extension and breakage of interatomic bonds at the tip of a propagating brittle crack is used to describe crack extension through a crystalline lattice by kink motion. Magnitudes of the effective kink barriers against crack extension and healing are computed as a function of lattice strain and are found to exhibit a marked asymmetry, relative to each other, in their strain dependences. In addition, decohesion effects associated with the presence of certain foreign atomic species are simulated, and it is shown that, for a broad range of relative bond-weakening, the kink barriers against both crack extension and healing are completely eliminated.     

A study of crack growth retardation due to artificially induced crack surface contact

The contact of the cracked surfaces during a part of a loading cycle generally results in a reduced crack growth rate. A critical experiment was designed to evaluate the influence of the crack surface contact on crack growth. A round compact specimen made of 1070 steel with a round hole at the wake of the fatigue crack was designed. Two mating wedges were inserted into the hole of the specimen while the external load was kept at its maximum in a loading cycle. In this way, the wedges and the hole in the specimen were in firm contact during the entire loading cycle in the subsequent loading. Experiments showed that the addition of the wedges resulted in a reduction of crack growth rate in the subsequent constant amplitude loading. However, crack growth did not arrest. With the increase in the subsequent loading cycles, crack growth rate increased. The traditional crack closure concept cannot explain the experimental phenomenon because the effective stress intensity factor range was zero after the insertion of the wedges. The detailed stress–strain responses of the material near the crack tip were analyzed by using the finite element method with the implementation of a robust cyclic plasticity theory. A multiaxial fatigue criterion was used to determine the fatigue damage based upon the detailed stresses and strains. The crack growth was simulated and the predicted results were in good agreement with the experimental observations. It was confirmed that the stresses and strains near the crack tip governed cracking behavior. Crack surface contact reduced the crack tip cyclic plasticity and the result was the observed retardation in crack growth.     

Application of fracture surface topographic analysis technique to thermal fatigue crack extension in stainless steel vessel

The fracture surface topographic analysis (FRASTA) technique is applied to investigate the propagating process of fatigue crack in a model vessel made of type 304 stainless steel due to repetitive thermal shocks for 1000 cycles. FRASTA is a procedure for reconstructing the process of crack extension by comparing topographic features of coupled areas of opposing fracture surfaces via computer. Based on the result, fracture mechanics analysis is made to estimate the relationship between crack depth and applied number of thermal cycles.

During the thermal transient test, acoustic emission (AE) is monitored using four channel AE sensors. The estimated number of initiating cycles and propagating behavior of macroscopic crack by fracture mechanics analysis is compared with the result of AE monitoring examination, and the usefulness of the FRASTA technique is discussed.     

Acoustic emission from crack growth in an advanced zirconia refractory under thermal shock

Crack initiation and growth during the thermal shock tests of a partially stabilized zirconia advanced refractory were investigated by the analysis of acoustic emission (AE) amplitudes. The growth of cracks that were detected by AE was systematically monitored by SEM observations as increasingly severe thermal shocks were applied. The measurements of strength loss after thermal cycling in the ribbon test with various applied temperature differentials correlated with continuous monitoring by acoustic emission and confirmed the effects of microcrack growth on the resistance to thermal shock damage.     

Cone crack initiation induced by contact from cylindrical punch

The critical load for cone crack initiation in a brittle material indented by a rigid cylindrical punch is related to the fracture toughness of the material and the punch radius through the classical energy principles. The strain energy required to form an embryo cone crack on a flaw-free surface adjacent to the punch edge is formulated, from which the critical load for cone cracking is then determined. The present analysis shows that the stress singularity close to the sharp contact edge is akin to that a sharp crack tip. The results in this study can be used to set up a simple and practical technique for evaluating some strength-related properties of brittle materials such as the fracture toughness.     

Features of fatigue crack growth due to repeated thermal shock

Abstract Thermal shock loading, such as that which occurs when a hot material is sprayed with cold water, produces a very high stress level near the exposed surface that eventually may lead to the development of cracks. Further growth of the cracks under repeated thermal shock is a very complex phenomenon due to the transient nature of the highly non-linear thermal stresses and the strong influence of the environment. There are cases in industry where cracks created by thermal shocks have arrested and stopped, and others where the cracks have progressed. Understanding this difference in behaviour is very important to the operators of pressure plant. This paper describes an experimental examination of crack growth in pressure vessel steel specimens exposed to repeated thermal shock. A test-rig that achieves large-scale thermal shocks through the repeated water quenching of heated flat plate specimens is used. The effect of steady-state loads on the growth is also analysed. Environmental effects due to the aqueous nature of the testing environment are found to be a major contributor to the crack growth kinetics.     

Elastic wave radiation from cleavage crack extension

The elastic waves, radiated from an isolated elastic microfracture of variable orientation and received at the epicentre of an elastic half-space, have been calculated and used to predict the acoustic emission signals that would be detected on various faces of a compact tension specimen. The displacements due to elastic waves radiated by incremental cleavage extension of precracks in such samples have then been measured, both ahead of and vertically above the advancing cracks. These acoustic emission signals are found to differ from the predicted waveforms because of the presence of precrack free surfaces, along which disturbances propagate from the crack tip at the surface wave velocity. Their effect is to increase the amplitude of the acoustic emission signal and enhance their lower frequency content. The experimental results are consistent with recent elastodynamic calculations of elastic radiation from incremental crack advance.

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Résumé On a calculé les ondes élastiques qui émanent d'une micro-rupture élastique et isolée d'orientation variable, et qui aboutissent à l'épicentre d'un demi-espace élastique. On a utilisé ces calculs pour prédire les signaux d'émission acoustique qui seraient détectés sur les diverses faces d'une éprouvette de traction compacte. Les déplacements associés aux ondes élastiques et créés par une extension progressive des clivages dans la zone de préfissuration de ces éprouvettes ont été mesurés, à la fois en avant de la fissure en propagation, et à la verticale de celle-ci. On trouve que les signaux d'émission acoustique diffèrent des formes d'ondes prédites en raison de la présence de surfaces libres de préfissuration le long desquelles se propagent des perturbations avec comme point de départ l'extrémité de la fissure et avec comme vitesse celle de l'onde de surface. L'effet en est d'accroître l'amplitude du signal d'émission acoustique et d'augmenter le contenu en fréquences faibles. Les résultats expérimentaux sont en accord avec les calculs élasto-dynamiques récents d'émission d'ondes élastiques à partir d'une fissure en propagation progressive.

     

Resistance to crack propagation in ceramics subjected to thermal shock

It is shown that the resistance to crack propagation in alumina, zirconia and porcelain, when subjected to thermal shock, is high when the initial strength is low and, vice versa when the initial strength is high. It is proposed that the high resistance to crack propagation results from discrete microcracking in the highly stressed zone ahead of the major crack, whereas the low resistance results from the unrestrained propagation of major cracks. Evidences of the crack patterns in alumina and zirconia substantiate this hypothesis.     

A finite element treatment of ductile crack extension

Abstract

To provide a realistic analysis for fracture, this paper is devoted to finite element approaches which attempt to describe ductile crack extension. A rigorous hybrid displacement finite‐element modeling, involving the translation of entire “singular” near‐tip elements and consideration of global energy balance, is successfully developed. To investigate the variation of global energy release rate G* and J‐integral for single‐step extensions at various levels of applied loads (extension ^δa = constant), the Kfouri et al.’s center‐cracked problem together with A533B compact tension specimen are solved. In addition, an available experimental J resistance curve for the compact tension specimen (made of Ni‐Cr‐Mo‐V rotor steel) is simulated by the present finite element analysis procedure to study the actual process of ductile fracture. The effect of unloading process occurred in the plastic region behind the advancing crack‐tip is also discussed.     

Flaking failure originating from a single surface crack in silicon nitride under rolling contact fatigue

Flaking failure caused by surface cracks of silicon nitride ceramic bearings has been investigated from the viewpoint of the ring crack model. However, the relation between surface and subsurface cracks under rolling contact fatigue is not fully understood. In this investigation subsurface cracks branching from an initial surface crack were observed in detail, and the process of flaking failure was investigated. The specimens were observed prior to the separation of the surface layers and it was found that the initial surface cracks grew vertically to the surfaces and did not curve as predicted by the ring crack model. Subsurface cracks branched from the single surface cracks and grew in a direction parallel to the surface. They grew in both the same and the opposite directions to the ball movement, with small upward and downward branches. These subsurface cracks grew prior to the semi‐circular surface cracks. From these observations it was concluded that the flaking failures are not caused directly by the surface cracks, but by the subsurface cracks that branch from them.     

Effect of crack shape,inclination angle,and friction coefficient in crack surface contact problems

In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle =15–30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for =45–90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions and polynomials. Then, a semi-elliptical crack model is analyzed for =15–90 under compressive residual stresses and Hertzian contact loads. The stress intensity factors K _II, K _III are calculated with varying the crack shape b/a, inclination crack angle , and crack face friction coefficient . The calculations show that the present method is useful for the analysis for =15–30 deg with high accuracy. It is seen that the K _II-values when b/a0 are larger than the ones when b/a=1 by 0–24% for both under compressive residual stress and Hertzian contact load. Regarding the maximum K _II values under Hertzian contact load, the results of =15 deg are smaller than the ones of =45 deg by 23–34%. Regarding the amplitude of (K _{II max}–K _{II min}), the results of =15 deg are smaller than the ones of =45 deg by 4–24%. With increasing the value of friction coefficient for crack faces the value of K _II decreases significantly. When the crack is short and the inclination angle is small, the value of friction coefficient f for Hertzian contact load largely affect the K _II value.     

A local approach model for cleavage fracture and crack extension direction of functionally graded materials

A local approach model has been developed for structural assessment of functionally graded materials in which the yield strength and the fracture toughness vary spatially. While the yield strength of the material at any point is taken to be deterministic, the local cleavage toughness is statistically distributed following a two-parameter Weibull model. The model is intended to determine the crack extension direction and failure probabilities of cleavage failure for a stationary pre-crack in a functionally graded material. The effect of independent variation in yield strength and toughness is discussed as a precursor to validating the model using a temperature gradient problem in which the yield strength and toughness are coupled through the temperature. The model is shown to closely reproduce experimental observations from cleavage fracture tests on mild steel subject to a controlled temperature gradient normal to the crack.