Conventional Fracture Mechanics Research Articles

A decagonal quasicrystal with a Griffith crack

Abstract The crack theory in conventional linear elasticity fracture mechanics is extended to quasicrystal linear elasticity fracture mechanics. A decagonal quasicrystal containing a Griffith crack penetrating through the solid along the period direction is considered. By means of a general solution, the analytical expressions for the entire stress field are obtained. The asymptotic behaviour of the stress around the crack tip indicates that the stress near the crack tip exhibits the square root singularity. The singularity in the phason stress field arises from that the phonon and phason fields couple with each other. The crack strain energy and energy release rate are also given.

An engineering method for constraint based fracture assessment of welded structural components with surface cracks

In this study it has been shown that accurate descriptions of crack-tip stress-fields in surface cracked welded plates can be obtained without large 3D FEA models. When a fracture mechanics FE analysis is required in a large construction, existing shell models can be used in combination with a plane strain submodel. The 2D plane strain model is driven by displacements from the global shell model. This technique has been used to simulate crack-tip stress-fields in a surface cracked plate. The crack-tip stress fields are characterised with the J-integral and the constraint parameter, Q. The crack in the global shell model was simulated with line-spring elements. The global behaviour as well as the crack-tip stress-fields of the plane strain submodel have been compared to a 3D solid model. Initially, the crack-tip stress-fields in the plane strain model and the 3D model with surface crack were compared, using the same in-plane mesh and element type. It was found that when first order elements were used, the constraint was higher in 3D than in plane strain. For second order elements, however, the trend was the opposite. By using a correction factor for the load, the load vs. J behaviour and the crack-tip stress-fields of a surface cracked plate can be predicted from a shell analysis with line-spring elements and a plane strain model. Accurate predictions of J and Q were obtained using the shell + submodel technique for homogeneous material and for a weldment with fusion line crack. The shell + submodelling technique was used to assess brittle fracture in two steel weldments with a surface crack using the RKR failure criterion by Ritchie et al. [16]. For the investigated case, the toughness requirements could be relaxed significantly based on the two parameter analysis compared to conventional fracture mechanics analyses.

Evaluation of Surface Damage and Residual Strength in Ceramics due to Sphere Impact. 2nd Report, Si3N4 Sphere Impact to Si3N4 Specimen-Elastic Analysis.

In the 1st report, it was shown that it was possible to apply an elastic indentation theory to the evaluation of surface damage of ceramics due to sphere impact, although this was limited to low velocities in which elastic damage dominated. In this research, further investigation on the applicability of the theory to the residual strength evaluation was conducted. In the case that elastic damage or cone crack was related in the final fracture, the residual strength of ceramic specimens damaged by sphere impact was estimated using the elastic indentation theory and conventional fracture mechanics. Good agreement between estimated curves and test results were obtained.

Investigation on the possibility of using the microshear test as a surveillance method to estimate the mechanical properties and fracture toughness of nuclear pressure vessel steel, A508CL3, and its joints welded by narrow-gap submerged-arc welding

The present paper has investigated the mechanical properties of nuclear pressure vessel steel, A508CL3, and its welded joints by using the microshear test method, and the fracture toughness of A508CL3 steel and its welds has also been estimated. Moreover, a comparison has been carried out between the conventional test, microshear test and fracture mechanics test. In addition, the possibility of using the microshear test on the surveillance program of nuclear pressure vessel embrittlement due to neutron irradiation has also been considered in detail, and the results indicate that the microshear test can be used successfully to estimate the degradation of mechanical properties both for A508CL3 steel and its welded joints. It has been found that the lower the microshear toughness, the smaller the Charpy V-notch (CVN) impact toughness and fracture toughness, as well as the tearing modulus. Finally, the results show that the microshear test method may be developed as a supplemental test method or standard of ASTM E185 and E636.

Local Approach to Brittle Fracture Strength Evaluation of Large Component with Shallow V-Notch

This paper employs the Local Approach for the evaluation of the fracture performance of a large structural component. The material used is a high strength steel of 490MPa class for steel-framed structures. Hollow-section beam specimens are constructed, where shallow V-notches are introduced at the edge of the flange. Conventional fracture mechanics procedures can not be directly applied to the notched component, because they have a basis on a crack or a crack-like defect. Three-dimensional FE-analysis demonstrates that the shallow V-notched component holds a considerably relaxed stress field compared to the fracture toughness specimen with a deep crack. This is due to a large difference in the near crack/notch tip constraint between the component and toughness specimen. This study insists that the Weibull stress, an integrated stress over the fracture process zone, is a measure of the fracture driving force of both notched and cracked specimens. The fracture load and fracture strain for the hollow-section beam with shallow V-notches can be predicted from the fracture toughness test results based on the Weibull stress criterion ; the critical Weibull stress at brittle fracture initiation is a material property regardless of the type of a notch/crack.

The fracture of poly(hydroxybutyrate) Part III Fracture morphology in thin films and bulk systems

This paper is the final part of a three paper series describing the fracture and ageing behaviour of poly(hydroxybutyrate). In the first two parts conventional fracture mechanics methods were used to monitor changes both during the detrimental room temperature ageing process that occurs and after a subsequent annealing process that had been reported to reverse the ageing process. This paper reports on our studies of the morphology of fracture surfaces and how fracture proceeds in different ways in the original, ductile, “fresh”, material, the more brittle, aged material and the ductile, annealed material. We have used optical and electron microscopic techniques to examine fracture surfaces of samples which had already been well characterised by mechanical testing. The effect of ageing and high temperature annealing on the resultant fracture morphology is detailed for both thin films and bulk samples. We have found that PHB undergoes crazing before failure regardless of annealing history. We have studied the craze morphology using optical microscopy and scanning electron microscopy. Both aged and un-aged samples are found to deform in approximately the same manner, the primary difference on ageing being the volume of material that is plastically deformed. After high temperature annealing a different craze morphology has been observed. In thin films this is characterised by the formation of a dense zone of micro-crazes over a relatively large area. In bulk samples there is a distinct change in the resultant fracture surface. In both thin films and bulk systems there is an increased occurrence of fracture initiation in the spherulite cores after high temperature annealing which helps to extend the craze zone.

Probing Fracture of Silicon Nitride by <i>In Situ</i> Microscopic Raman Spectroscopy

In situ Raman microprobe spectroscopy has for the first time provided direct experimental evidence that Si3N4 is toughened by virtue of local microscopic bridging stresses operated by unbroken grains, which resist crack opening upon external load. The bridging stresses may arise from elastic tractions of unbroken Si3N4 grains which bridge the crack in the very neighborhood behind its tip, or be of frictional nature at the grain interfaces in regions more far behind the tip. Particularly remarkable is the magnitude of the elastic bridging tractions which achieve the GPa order prior to microscopic fracture of the bridging site. Frictional tractions in correspondence of elongated Si3N4 grains may also locally achieve the order of several hundreds MPa, but they are shown to contribute toughening in a less effective way as compared to elastic bridges. Conventional fracture mechanics characterization and theoretical considerations are also provided which prove the rising R-curve effect in Si3N4 ceramics being explainable simply in terms of the microscopic crack bridging mechanism.

Elastic Compliance of the Compact Tension Specimen Comprising Two Linear-Elastic Materials Bonded with a Thin Layer

Abstract Although the compact-tension C(T) specimen is widely used in conventional fracture mechanics testing, its application to the fracture behavior of layered structures, in the assessment of the toughness and fatigue crack growth behavior of bimaterial interfaces, for example, has been limited due to problems in identifying the crack length. Accordingly, to provide a basis for crack-length monitoring in the sandwich C(T) specimen, comprising two materials bonded with a thin layer under linear-elastic conditions, the linear-elastic compliance based on back-face strain, crack-opening displacement and load-line displacement has been determined for a wide range of substrate/layer material combinations using finite-element analyses. Calculations for sandwich systems, with elastic moduli ratios varying from 0.2 to 5 and with joining layer thicknesses between 0.4 and 2% of the specimen width, show that for crack sizes between 0.25 to 0.75 of the specimen width, the compliance is significantly different from that of the bulk substrates, except when the layer is very thin and the modulus ratio approaches unity. It is concluded that crack-opening displacements are preferable for the monitoring and detection of interfacial and near-interfacial cracks in this specimen geometry, as the compliance based on these displacements is the least sensitive to errors from either measurement site or crack location.

Creep Rupture Investigation of 63Sn-37Pb Solder by Experiments and Damage Mechanics

Abstract The main purpose of this paper is to investigate the crack growth path and creep rupture life of 63Sn-37Pb bulk solder experimentally by Moiré analysis and theoretically using continuum damage mechanics. In conventional fracture mechanics analysis, a crack growth path is assumed a priori. Fracture parameters such as the J-integral and stress intensity factor are subsequently calculated to predict the crack growth rate and structural life. However, it is often difficult to postulate the correct crack growth path for a complex structure that is subject to complex loading. Continuum damage mechanics is an alternative method that can be used to compute structural life with the important feature that the crack growth path is computed automatically. In this paper we develop a theory for partially reversible creep-fatigue damage. A finite element procedure incorporating this damage theory is developed and used to analyze the response of bulk solder plates with holes. The displacement fields obtained by finite element analysis are compared to the fringe patterns obtained from conventional Moiré experiments. Furthermore, the accuracy of the predicted crack growth paths was investigated by comparison between the maximum damage contours obtained by finite element simulation with the actual crack paths occurring in the laboratory specimens. These comparisons indicate the new continuum damage theory developed herein can adequately predict creep displacements, crack growth paths, and structural life.

Examination of the fatigue crack growth equations

Most of the crack growth equations proposed so far correlate the crack growth rate (da/dN or da/dt) with crack tip parameters such as the stress intensity factor (SIF) or energy release rate (ERR). In our previous works, an experimental setup was designed to examine the applicability and the boundary of the functional relationship between da/dN and the crack tip parameters, particularly, ERR. In the present paper, the variation of the ERR along the experimentally observed curvilinear crack trajectories is obtained by means of the finite element method. The analysis shows that the Paris-Erdogan type of laws are applicable until the crack tip is located outside the strong crack-defect interaction region (SI region). A functional relationship between da/dN and ERR breaks down within this region. This suggests the existence of additional crack tip parameters that are not accounted for within conventional fracture mechanics. An approach to modeling the observed phenomenon is discussed following the concept of the Crack Layer theory.

ローカルアプローチの適用によるぜい性破壊発生限界に及ぼす試験片形状・寸法の影響の評価

The effects of specimen geometry and loading mode on the resistance to brittle fracture initiation were analyzed by the local approach. The fracture resistance of materials under a large scale yielding condition evaluated by the conventional fracture mechanics parameters, such as crack tip opening displacement (CTOD), depends to a large extent on the specimen geometry and loading mode. This is due to the geometrical constraint effect on the crack tip stress field. The three-dimensional FE analysis figured out that, as plasticity developed, a shallow notch bend specimen and tension specimens (CCP and DECP) showed significant loss of constraint compared to a deep notch bend specimen. This led to a lower stress near the crack tip for the shallow notch bend specimen and tension specimens than the deep notch bend specimen. By contrast, the critical Weibull stress at brittle fracture according to the local approach did not depend on the geometry of specimens used. This paper demonstrates the independence of the critical Weibull stress on the crack depth of 3-point bend specimen. As an advantage, the local approach enabled us to predict the specimen geometry effect on the critical CTOD at fracture.The effects of specimen geometry and loading mode on the critical CTOD at fracture depend on the hardenability of materials. In the case of high hardening materials, the critical CTOD is not very sensitive to the specimen geometry and loading mode excepting the thickness effect on the critical CTOD for materials with a large scatter in toughness. On the other hand, for low hardening materials, the critical CTOD is affected to a large extent by the crack depth and loading mode of specimens.

Damage development in a sidegrooved CT specimen based on a 3-D endochronic damage model

This paper presents a three-dimensional crack initiation analysis in a sidegrooved CT specimen. This is achieved with an endochronic damage model proposed recently by Chow and Chen ( 1,2) and discretized for finite element analysis. The damage model enables the quantification of the progressive damage evolution which would not be otherwise possible using the conventional fracture mechanics analysis. By employing two separate damage failure criteria, the crack is predicted to initiate at a small distance from the sidegroove and the prediction agrees well with the experimental observation. A more uniform crack initiation across the crack-tip line is observed both experimentally and theoretically relative to the CT specimen without sidegrooving.

DYNAMIC CRACK PROPAGATION AND CRACK ARREST BEHAVIOUR IN RELATION TO BRITTLE INTERGRANULAR AND CLEAVAGE FRACTURE

Abstract— Conventional mechanical tests and fracture mechanics experiments were carried out at – 196°C on a low alloy steel (A508 class 3) which was investigated under two different conditions: (i) a reference condition in which the failure mode was cleavage and (ii) an embrittled condition in which the fracture mode was either partly or predominantly intergranular fracture. These experiments, performed with a new specimen geometry, a ring specimen instrumented to measure also the crack velocity, were used to determine the fracture toughness at crack initiation (KIc) and at crack arrest (KIa). It is confirmed that the reduction in KIc measured in the embrittled material is associated with the appearance of intergranular fracture. It is also shown that KIa, determined by a static analysis decreases rapidly with crack velocity when the fracture mode is predominantly cleavage. On the other hand, KIa, corresponding to intergranular fracture seems to be much less dependent on crack speed. This difference in the sensitivity of both modes of brittle fracture to crack velocity is briefly discussed.

An Experimental and Analytical Study of Delamination of Unidirectional Specimens with Cut Central Plies

The effect of various factors on delamination has been studied using uni directional glass fibre and carbon fibre-epoxy specimens with cut central plies. It is con cluded that the fracture energy is not a material constant. Among the various factors which affect the fracture energy, the specimen thickness and the through thickness normal stress are the two most significant ones. A simple model is proposed to take account of these two factors. The new model gives excellent correlation with experimental results and is able to account for the effect of through thickness compressive stresses in mode II fracture, which is ignored in conventional fracture mechanics calculations.

Fatigue crack propagation in single-crystal CMSX- 2 at elevated temperature

The fatigue crack propagation (FCP) behavior of the nickel-base superalloy CMSX-2 in single-crystal form was investigated. Tests were conducted for two temperatures (25 and 700 °C), two orientations ([001][110] and [001][010]), and in two environments (laboratory air and ultra-high vacuum 10-7 torr). Following FCP testing, the fracture surfaces were examined using scanning electron microscopy (SEM). The FCP rates were found to be relatively independent of the temperature, environment, and orientation when correlated with the conventional mode I stress-intensity factor. Examination of the fracture sur-faces revealed two distinct types of fracture. One type was characterized by 111 fracture surfaces, which were inclined relative to both the loading and crack propagation directions. These features, al-though clearly a result of the fatigue process, resembled cleavage fractures along 111 planes. Such fea-tures were observed at 25 and 700 °C; they were the only features observed for the 25 °C tests. The second type had a macroscopically dull loading appearance, was microscopically rough, and grew normal to the loading axis. These features were observed on the specimens tested at 700 °C (in both air and vacuum) and appeared similar to conventional fatigue fractures. Although in this region the crack plane was mac-roscopically normal to the loading direction, it deviated microscopically to avoid shearing the y ’ precipi-tates. In view of the complex crack growth mechanisms, mixed fracture modes, and lack of any difference in FCP rates, it is hypothesized that the correlation between FCP rates and the stress-intensity parameter is probably coincidental. The implications for life prediction of higher temperature turbine components based on conventional fracture mechanics are significant and should be investigated further.

Effect of shot peening on fatigue behavior in aluminum alloys: Wagner, L. and Mueller, C. Mater. Manuf. Proc. 1992 7, (3), 423–440

Suitability of different multi-axial parameters in predicting fretting fatigue life of Ti–6Al–4V specimens has been investigated. Ameliorating effect of surface treatments on fretting fatigue has been studied. In simple uni-axial/multi-axial fatigue tests, nucleation as well as propagation of cracks occur under the influence of identical stresses. Hence nucleation accounts for most of the total life. Fretting fatigue crack nucleation occurs due to very large contact stresses, effect of which is felt only close to the surface (due to steep gradients). Propagation mostly occurs due to lower stresses in the bulk of the material (negligible influence of contact tractions) and forms a significant portion of total life. Total life has to be taken as sum of initiation life calculated from different multi-axial fatigue parameters and propagation life from conventional fracture mechanics approach. Steep stress gradients necessitate the adoption of a statistics based approach to predict the crack initiation life, based on an assumed distribution of flaws. The quality of comparison between predicted and experimentally observed failure lives provides confidence in the notion that conventional fatigue life prediction tools can be used to assess fretting fatigue failure. Effect of surface treatments like shot-peening with or without additional surface coatings on total life of the specimen and on friction coefficient has been studied.

Relationship between Fracture Surface Roughness and Fracture Behavior of Cement Paste and Mortar

Fracture surfaces of cement and mortar specimens were characterized using a confocal microscope to create three‐dimensional computer‐based topographic maps. The texture of the fracture surfaces was quantified using image analysis techniques to compute a roughness parameter and fractal dimension. Total porosity, pore‐size distribution, compressive strength, and fracture properties of the specimens were determined and compared with the roughness parameter. Fracture properties were determined by notched‐beam tests and the results were analyzed both by using conventional linear elastic fracture mechanics as well as a compliance‐based approach that incorporated R‐curve type of behavior. A positive correlation between fracture surface roughness and fracture toughness was demonstrated.

Effect of a Microdefect ahead of a Main Crack on Strength of Solids.(1st Report, Approximate Solution in Terms of a Main Crack Stress Field).

Recently, it has been reported that the fracture stress σf and the fracture toughness Kc of engineering ceramics, measured by use of short precracks, have values lower than, σf = KIC/(πc)1/2 and KC = KIC, which might be expected from the conventional fracture mechanics. In the present study, assuming that these phenomena are due to the effect of a microdefect formed ahead of a main crack under applied stress, we propose a main crack-microdefect interaction model and formulate it using the theory of continuous distribution of dislocation in order to explain the above experimental results. As a result, we obtain the stress intensity factor K at the tip of the microdefect in a closed form. Supposing that macroscopic fracture would be caused when the stress intensity factor K reaches the plane-strain fracture toughness KIC, we can obtain the analytical expressions of the fracture stress σf and the fracture toughness Kc and explain the above phenomena theoretically.

Influence of orientation on the low cycle fatigue of MAR-M 200 single crystals at 650 °C I: Fatigue life behaviour

Low cycle fatigue tests on MAR-M 200 single crystals were conducted at 650 °C under total axial strain control. Specimens having crystallographic orientations near [001], [111], [213] and [101] were tested under fully reversed strain. Fatigue life-total strain range curves were strongly orientation dependent but this behaviour was mainly due to variations in Young's modulus with orientation. Crack initiation occurs at MC particles at high plastic strain ranges where slip bands formed in the overall specimen gauge length. At longer lives, cracks initiate at subsurface micropores. The most part of fatigue life is spent in stage II crack propagation as shown by plastic replicas and metallographic observations of specimens. Fatigue life was thus predicted using a local approach to fracture and crack growth data from conventional compact tension fracture mechanics specimens.

A continuum damage mechanics model for crack initiation in mixed mode ductile fracture

This paper presents the development of a fracture criterion based on the postulation that the threshold condition of crack initiation in mixed mode ductile fracture is satisfied when the overall damage w in an element at the prospective direction of crack path reaches its critical value wc. The validity of the proposed criterion is checked by predicting the fracture loads of thin aluminium plates containing an isolated crack inclined at the angle of β=30, 45, 60 and 75 degrees and the predicted loads are compared satisfactorily with those determined experimentally. The analysis is performed based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors, thus providing additional proof of the consistency, applicability and versatility of the model. When the fracture loads of the mixed mode plates calculated using conventional fracture mechanics are compared with those determined using the proposed damage model, a maximum close to 30 percent over-estimation of the loads from the conventional approach is observed as opposed to within 7 percent discrepancy between the computed and measured fracture loads using the damage approach. The observation reveals the importance of including damage consideration in any ductile fracture analysis.