Two-parameter Fracture Mechanics Research Articles

Fracture prediction of solder joints using two-parameter fracture mechanics

Two-parameter fracture mechanics theory is a novel approach to investigate the fracture behavior of solder joints. The present study showed that the single-parameter fracture mechanics was not valid for evaluating the fracture behavior of these joints. Therefore, the ability of the two-parameter (J-Q) fracture mechanics method was assessed. J (critical strain energy release rate) and Q (The constraint parameter) parameters were calculated for the double cantilever beam (DCB) specimens. The two-parameter fracture mechanics theory was observed to be valid for the DCB specimens examined in this research. The J-Q loci extracted from two distinct experimental data sets (adherend thickness and loading arm variation) were coincident. The overlap of two J-Q locus curves indicates the uniqueness of the J-Q locus and capability to predict fracture load.

Two-parameter elastic-plastic fracture criterion and corrected fracture toughness

The basic aspects of the J-A concept of elastic-plastic two-parameter fracture mechanics, based on a three-term asymptotic description of the stress field at the crack tip are presented. It is noted that the field of elastic-plastic stresses at the crack tip is controlled by two parameters of fracture mechanics, namely, J-integral and parameter A. Parameter A is a measure of the deviation of the stress field from the HRR-stress field and can be considered a parameter of elastic-plastic constraint at the crack tip both under conditions of small- and large-scale yielding. The results of studying the influence of the exponent of the strain hardening of the material, crack aspect ratio and the thickness of standard specimens with a crack on the elastic-plastic stress intensity factor and parameter A are presented. A two-parameter elastic-plastic J-A fracture criterion based on the relationship between J-integral and strain(stress) on the surface of the crack-notch and the principle of linear summation of damage is formulated. To reflect the crack-tip constraint, the parameter A is introduced into the criterion equation as a function of applied failure stresses. The elastic-plastic fracture toughness as a function of the crack-tip constraint in the fracture criterion is interpreted as the corrected elastic-plastic fracture toughness of a specimen with the corresponding constraint parameters A. The results of studying the normalized corrected fracture toughness as a function of failure stresses, crack aspect ratio and strain hardening exponent of the material are presented.

Interaction of crack-tip constraint and welding residual stresses on the fracture behavior of Ni-based alloy

The present paper aims to study the effect of crack-tip geometrical constraints and welding residual stresses (WRS), as well as their interaction on fracture behavior of IN939 superalloy, which is widely used in gas turbine hot section components, such as turbine vanes. For the thermal–mechanical simulation of welding processes, a finite element (FE) model was developed, and the predicted WRS was verified through experiments. Two welding paths and two mechanical boundary conditions were considered to develop four different WRS distributions within the same geometry. These results were mapped to the validated fracture finite element models. By varying the loading conditions, two sets of specimens with high and low geometrical constraints were achieved in the same geometry. Two-parameter fracture mechanics analyses were then used to examine the effects of four WRS profiles and geometrical constraints on the fracture behavior of each set. Generally, the impact of WRS is more evident in specimens with lower geometrical constraints. The fracture behavior might be unexpectedly affected if the WRS changes from tensile to compressive near the crack tip. Using the maximum stress triaxiality factor, it was shown that the fracture behavior as a function of WRS is better demonstrated than that of the Q-constraint parameter.

Automatic Crack Tip Meshing Approach for Constraint-Based Fracture Mechanics Application

Finite element analysis is a popular method used to characterize crack tip stress and strain fields in fracture mechanics problems. In a constraint-based elastic-plastic fracture mechanics, the crack tip stress and strains are essentially dependent on the accurate crack tip finite element configuration. Typical finite element software does not provide control of node and elemental numbering order and sequence which caused difficulty to examine different crack configuration state of stress–strain using automated post-processing codes. A method to automate the creation of finite element mesh of arbitrary lengths and shapes of standard and nonstandard fracture mechanics geometries using a geometric progression technique is described. A list of equations was proposed to develop nodal and elemental model data that represented a defined region of a cracked geometry. Assembly of the regions produced a finite element mesh representing a fracture mechanics cracked geometry which can be incorporated into a typical finite element program. The approach can eliminate the modeling processes of finite element of cracked specimens and offers the ability to control the nodal and elemental numbering system to allow systematic stress and strain elucidation for large degrees of freedom mesh and history-dependent incremental plasticity crack tip analysis. The approach used to develop the finite element mesh was discussed, and examples of the finite element mesh generated by the approach were compared to established two-parameter elastic-plastic fracture mechanics results. Finally, the algorithm codes used to develop the cracked models are supplied as supplementary files to interested users.

A comparison between two parameter and ductility exhaustion approaches for creep life assessment

To improve the accuracy of creep life assessment for cracked components, the two-parameter fracture mechanics approaches with considering the constraint effect have been investigated and developed over the past decade. To examine the accuracy and applicability of different approaches, in this work, the creep life (including both creep crack initiation and growth life) is comparatively assessed using the two-parameter C*-R*, two-parameter C*-Ac and ductility exhaustion based approaches for pressurized pipes with different initial axial crack sizes. The results show that the life assessment results of the C*-R* approach are sensitive to initial crack sizes. For the shallower initial cracks, the C*-R* approach can give reasonable life prediction results, while for the deeper and longer cracks, it produces conservative results due to the sensitivity of the in-plane constraint parameter R* to initial crack sizes. The ductility exhaustion based approach verifies that the two-parameter C*-Ac approach has better life prediction accuracy for a wide range of initial crack sizes due to that the parameter Ac can characterize both in-plane and out-of-plane constraints and it is not very sensitive to initial crack sizes. The C*-Ac approach also can accurately predict the creep crack growth morphology which is mainly dependent on the initial crack aspect ratio.

Corrosion effect, constraint and path orientation estimated in cracked gas turbine blade

The severe damage of gas turbine is due to the failure of the blade, in which the occurrence of a serious pitting occurred on the blade surfaces was evidence of fatigue marks in the fracture surface. This paper deals with the effect of semi-elliptical crack propagation on the crack path using a basic approach in predicting crack paths, namely, incremental methods. The crack position was chosen at the node coordinate where we have the maximum principal stresses. In this node, we have created a semi-elliptical crack and we have compared the results with the Stress Intensity Factors and T-stress values. The local fracture criterion of the maximum average tangential stress in the vicinity of fracture process zone including two terms of the Williams series solution for the mixed mode I/II loading has been used for predicting the angle of surface crack growth. The volumetric method (VM) for the compression-sensitive materials is described by a linear combination of the effective stress and the effective stress intensity factor. The results of our finite element computations based on a two-parameter fracture mechanics formulation showed that the T-stress has significant effects on the crack path.

Validating 3D two-parameter fracture mechanics models for structural integrity assessments

In-situ fracture tests were carried out on the I12 beamline at the Diamond Light Source. Four Al-Ti metal-matrix composites, with two crack lengths, were studied to assess for the impact of in-plane constraint. Synchrotron X-ray computed tomography and synchrotron X-ray diffraction were used to measure total strain and elastic strain respectively. In this work, the measured elastic strains in the samples are detailed as a function of applied load and compared against those predicted from a 3D elastic-plastic finite element model. The modelled strains increased asymptotically towards the tip of the electro discharge machined notch. The experimental results do not highlight the same response, which is due to a combination of blunting and low experimental spatial resolution. Far field experimental and measured strain fields converged, notably in the test piece containing a long notch (a/W = 0.5) and higher levels of constraint.

Three-dimensional assessments of crack tip constraint

Crack tip constraint can be used as a means to relate the stresses at the crack tip to a measure of fracture toughness of a material. Current technique to determine crack tip constraint demonstrated in structural integrity standards are based on two-dimensional plane strain approach. This paper explores the possibility of extending the current two-dimensional crack tip constraint solutions to three-dimensional crack problems through an investigation of the asymptotic structure of three-dimensional crack tip stress fields under elastic-plastic non-hardening responses. Analysis was based on three-dimensional boundary layer formulations, combined with full-field solutions of single edge notched bend bars and centre cracked tension panels having a range of thicknesses. The fields along the crack front were examined as a function of load level and thickness. From the results, it is demonstrated that, at the crack tip (r = 0), a family of asymptotic fields develop which feature a constant stress sector directly at the crack tip. Within this sector the fields differ hydrostatically while being similar in respect of the maximum stress deviator. At the intersection with the free surface, an elastic perfectly-plastic corner field which differs from the plane stress field is shown to develop. It is shown that in these fields the level of constraint is parameterised by J/zσo, where z is the distance from the free surface. J/zσo unifies both the change in the maximum principal stress and the mean stress, as a function of thickness and deformation level from all sections of different geometry and thickness specimens. An explicit expression has been developed which demonstrated the constraint loss due to in-plane and out-of plane crack tip constraint effects, allowing a two-parameter fracture mechanics methodologies in a modified form to be extended to fully three-dimensional fields.

Validating 3D two-parameter fracture mechanics for structural integrity assessments

In-situ fracture tests were carried out on the I12 beamline at the Diamond Light Source. Four Al-Ti metal-matrix composites (MMCs), with varying combinations of thickness and crack length, were studied to assess for the impact of in-plane and out-of-plane constraint. Synchrotron X-ray computed tomography and synchrotron X-ray diffraction were used to measure total strain and elastic strain respectively. The total strain was calculated via digital volume correlation, with Ti particles within the MMC providing sufficient texture to track the internal displacement vectors in 3D. The total, elastic-plastic strain energy release rate, Jtotal was calculated from 2D slices extracted from the 3D displacement field, with Jtotal reaching a maximum value at the sample surface. It is, however, still unclear whether calculating Jtotal on a slice-by-slice basis provides an accurate representation of strain energy release rate across the crack front; techniques to evaluate the J-integral from the full 3D displacement field are being developed.

A Two Parameter Fracture Mechanics Approach to Analyze Threaded Fasteners of A High Strength Steel

This paper presents a numerical investigation using the two-parameter fracture mechanics approach for studying threaded fastener geometries. It was found that the constraint arising from the presence of a surface crack in a threaded fastener does influence the stress in the forward sector.

Effects of the Crack Tip Constraint on the Fracture Assessment of an Al 5083-O Weldment for Low Temperature Applications.

The constraint effect is the key issue in structural integrity assessments based on two parameter fracture mechanics (TPFM) to make a precise prediction of the load-bearing capacity of cracked structural components. In this study, a constraint-based failure assessment diagram (FAD) was used to assess the fracture behavior of an Al 5083-O weldment with various flaws at cryogenic temperature. The results were compared with those of BS 7910 Option 1 FAD, in terms of the maximum allowable stress. A series of fracture toughness tests were conducted with compact tension (CT) specimens at room and cryogenic temperatures. The parameter for the Al 5083-O weldment was evaluated to quantify the constraint level, which is the difference between the actual stress, and the Hutchinson-Rice-Rosengren (HRR) stress field near the crack tip. Nonlinear 3D finite element analysis was carried out to calculate the parameter at cryogenic temperature. Based on the experimental and numerical results, the influence of the constraint level correction on the allowable applied stress was investigated using a FAD methodology. The results showed that the constraint-based FAD procedure is essential to avoid an overly conservative allowable stress prediction in an Al 5083-O weldment with flaws.

The effect of residual stress on the nonsingular T-stresses

The effect of residual stresses on surface fatigue crack propagation and fracture mechanics parameters of intersecting orthogonal cracks is discussed. Mutual influence of intersecting cracks and biaxiality affects the nonsingular parameters Txx and Tzz. At the same time, the effect on the stress intensity factor is negligible. Two-parameter fracture mechanics is employed for an analysis of fatigue crack propagation taking into account residual stresses. The final configuration of the crack front is close to the semi-elliptical configuration.

T-stress estimation by the two-parameter approach for a specimen with a V-shaped notch

In the present research, T-stress solutions are provided for a V-shaped notch in the case of surface defects in a pressurised pipeline. The V-shaped notch is analyzed with the use of the finite element method by the Castem2000 commercial software to determine the stress distribution ahead of the notch tip. The notch aspect ratio is varied. In contrast to a crack, it is found that the T-stress is not constant and depends on the distance from the notch tip. To estimate the T-stress in the case of a notch, a novel method is developed, inspired by the volumetric method approach proposed by Pluvinage. The method is based on averaging the T-stress over the effective distance ahead of the notch tip. The effective distance is determined by the point with the minimum stress gradient in the fracture process zone. This approach is successfully used to quantify the constraints of the notch-tip fields for various geometries and loading conditions. Moreover, the proposed T-stress estimation creates a basis for analyzing the crack path under mixed-mode loading from the viewpoint of the two-parameter fracture mechanics.

A transferability approach for reducing excessive conservatism in fracture assessments

A source of uncertainty and conservatism in structural integrity assessments is the value of fracture toughness (Kmat) that is used. For conservative results, the value of Kmat is commonly derived from deeply cracked specimens, such as standard compact tension specimens, C(T). High constraint conditions near the crack tip are ensured and this corresponds to lower-bound toughness values independent of specimen size and geometry. However, the local stress fields in single edge notched tension, SE(T), specimens and pipes, for example, are known to be less severe than those at the tip of a deep sharp crack, resulting in an increased capacity to sustain load and higher toughness. Similar behaviour is expected when assessing non-sharp defects (e.g., pits, gouges, dents). The constraint loss or the notch effect produce a relaxation in the triaxial stress field in comparison to the severe stress fields present at deeply sharp cracked specimens. A methodology providing a simple procedure to evaluate the suitability of the use of a higher fracture toughness to reduce excessive conservatism is then required. This study uses a two-parameter fracture mechanics approach (J-Q) to quantify the level of constraint in a component (e.g. a pipe with a surface crack) and in fracture test specimens, i.e. single edge tension [SE(T]), standard compact tension [C(T)] and notched compact tension [C(T)ρ] specimens. The ability of the structure to resist fracture is given by the fracture toughness of the test specimen with a similar J-Q response. Fracture toughness values for different specimens have been obtained from tearing resistance curves (J-R curves) constructed by means of a virtual testing framework. The proposed engineering approach is used as a platform to perform more accurate fracture assessments by the use of a ductile fracture model that informs a classical fracture mechanics approach (J-Q) by incorporating more fundamental understanding of the driving forces and the role of the geometry and loading conditions.

Ductile fracture modelling and J-Q fracture mechanics: a constraint based fracture assessment approach

The reduced state of stress triaxiality observed in shallow cracked components allows an increased capacity to resist crack propagation compared to that observed in deeply cracked specimens. This may be regarded as a higher fracture toughness value which allows a reduction in the inherent conservatism when assessing components in low constraint conditions. This study uses a two-parameter fracture mechanics approach (JQ) to quantify the level of constraint in a component (e.g. a pipe with a surface crack) and in fracture test specimens, i.e. single edge tension [SE(T]) and compact tension [C(T)] specimens, of varying constraint level. The level of constraint of the component is matched to a specific test specimen and therefore the ability of the structure to resist fracture is given by the fracture toughness of the test specimen with a similar J-Q response. Fracture toughness values for different specimens have been obtained from tearing resistance curves (J-R curves) constructed by means of a virtual testing framework. The proposed engineering approach shows that the combination of a local approach and two-parameter fracture mechanics can be used as a platform to perform more accurate fracture assessments of defects in structures with reduced constraint conditions. KEYWORDS. Crack tip constraint; Ductile fracture modelling; J-Q fracture mechanics.

Drilling Repair Index (DRI) based on two-parameter fracture mechanics for crack arrest holes

The most common method of preventing cracks from growing is by making a “drill stop” or crack arrest hole (CAH) at the crack tip. The objective of drilling a hole is to “blunt” the crack tip and reduce the stress concentration at the crack tip. In this paper the following situations are studied: (i) a single hole drilled at a blunt crack tip, (ii) a single hole drilled at a distance r from the crack tip with an orientation angle θ relative to the crack direction and (iii) a second hole called the “stress concentrator reducer hole” drilled symmetrically to the first near to the crack hole. A Drilling Repair Index (DRI) is proposed for evaluation of the efficiency of the CAH method. It is based on two-parameter fracture mechanics.

Prise en charge de la rhinite allergique : une question d’actualité

The most common method of preventing cracks from growing is by making a “drill stop” or crack arrest hole (CAH) at the crack tip. The objective of drilling a hole is to “blunt” the crack tip and reduce the stress concentration at the crack tip. In this paper the following situations are studied: (i) a single hole drilled at a blunt crack tip, (ii) a single hole drilled at a distance r from the crack tip with an orientation angle θ relative to the crack direction and (iii) a second hole called the “stress concentrator reducer hole” drilled symmetrically to the first near to the crack hole. A Drilling Repair Index (DRI) is proposed for evaluation of the efficiency of the CAH method. It is based on two-parameter fracture mechanics.

The concept of averaging of stresses in the problems of the two-parameter fracture mechanics

The article illustrates the application of the Neuber-Novozhilov concept for averaging of stress to before tip of a crack/cutout in solving of contemporary problems of two-parameter fracture mechanics, aimed at creation of models and criteria of body limit state and search of a crack path. As a parameters of tightness strain in the vicinity of the crack tip are used nonsingular components of T-stresses of the stress field.

Understanding and accounting for the effects of residual stresses on cleavage fracture toughness measurements in the transition temperature regime

Secondary self-balancing stresses exist in structural components due to manufacturing processes, e.g. welding. When a defect is present, such secondary stresses will influence both the local crack driving force and the level of crack-tip constraint. Fracture mechanics specimens machined from welded components can also retain significant residual stresses, and these can influence the measurement of fracture toughness. This paper describes the results of an experimental and numerical programme aimed as quantifying the effect of residual stresses on cleavage fracture toughness measured in deeply-cracked and shallow-cracked fracture mechanics specimens and with a view to correcting the resultant data. The results indicate that the influence of retained residual stresses on cleavage fracture toughness in such specimens can be characterised using two-parameter fracture mechanics.

Wedge splitting test method: quantification of influence of glued marble plates by two-parameter fracture mechanics

In the present paper, the well-known wedge splitting test (WST) is applied on specimens with different geometries (S= 150, 200, 300 mm) and variants of the specimens’ configurations. K-calibration (B1) and T-stress (B2) calibration curves for such specimens are introduced. The objective was to compare and discuss the values of the calibration curves dependent on the specimen’s geometries and on three different specimens' configurations: homogenous specimen; specimen with marble plates forming the groove for load application and specimen with glued marble plates.