Showing papers on "Crack closure published in 2002"

Strength or toughness? A criterion for crack onset at a notch

Abstract: Both energy and stress criteria are necessary conditions for fracture but neither one nor the other are sufficient. Experiments by Parvizi et al. on transverse cracking in cross-ply laminates corroborate this assumption. Thanks to the singularity at the tip of the notch, the incremental form of the energy criterion gives a lower bound of admissible crack lengths. On the contrary, the stress criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation. It enjoys the desirable property of coinciding with the usual Griffith criterion to study the crack growth and with the stress criterion for the uniform traction along a straight edge. Comparisons with experiments carried out on homogeneous notched materials and on bimaterial structures show a good agreement.

Effect of Simulation Methodology on Solder Joint Crack Growth Correlation and Fatigue Life Prediction

Abstract: A generalized solder joint fatigue life model for surface mount packages was previously published in Refs [1,2]. The model is based on correlation to measured crack growth data on BGA joints during thermal cycling. It was subsequently discovered by Anderson et.al. that the ANSYS 5.2 finite element code used in the model had an error in its method for calculating plastic work [3]. It was shown that significant error in life prediction could result by using a recent version of the code where the bug has been fixed. The error comes about since the original crack growth constants were derived based on plastic work calculations that had the bug. In this paper, crack initiation and growth constants are recalculated using ANSYS 5.6. In addition, several other model related issues are explored with respect to the crack growth correlations. For example, 3D slice models were compared to quarter symmetry models. Anand’s constitutive model was compared with Darveaux’s constitutive model. It was shown that the crack growth rate dependence on strain energy density always had an exponent of 1.10 +/0.15. This is in the range of the original correlation, so the accuracy of relative predictions should still be within +/25%. However, the accuracy of absolute predictions could be off by a factor of 7 in the worst case, if the analyst uses a modeling procedure that is not consistent with that used for the crack growth correlation. The key to good accuracy is to maintain consistency in the modeling procedure. Introduction Analytical models in engineering have several practical uses: 1) rapid design optimization during the development phase of a product, 2) predicting field use limits, and 3) failure analysis of product returned from the field or failed in a qualification test. The solder joint fatigue model presented here was first published in Ref [1]. An outline of the procedure to predict fatigue life is shown schematically in Figure 1. The model utilizes finite element analysis to calculate the inelastic strain energy density accumulated per cycle during thermal or power cycling. The strain energy density is then used with crack growth data to calculate the number of cycles to initiate a cracks, and the number of cycles to propagate cracks through a joint. In reference [2], more work was presented regarding sensitivity of the life prediction to the FEA procedure. As a result, the procedure was modified slightly to include volume averaging of the strain energy values near the joint interface. The model has been successfully applied to TSOP, CQFP, CBGA, PBGA, and power hybrid packages [1,2,4-9]. Calculate Strain Energy Density Accumulated per Cycle Calculate Number of Cycles to Crack Initiation Calculate Crack Growth Rate Calculate Fatigue Life Based on Joint Length Figure 1. Solder joint fatigue life prediction method. It was subsequently discovered by Anderson et.al. that ANSYS 5.5.2 and earlier versions of the finite element code had an error in their method for calculating plastic work [3]. Even though there had generally been good correlation to measured results, it was shown that significant error in life prediction could result by using a recent version of the code where the bug has been fixed (e.g. ANSYS 5.5.3 and later versions). The error comes about since the original crack growth constants were derived based on plastic work calculations that had the bug. In this paper, crack initiation and growth constants are recalculated using ANSYS 5.6. In addition, several other model related issues are explored with respect to the crack growth correlations. Several recommendations are made so the analyst can get accurate results more efficiently. Constitutive Relations Since solder is above half of its melting point at room temperature, creep processes are expected to dominate the deformation kinetics. Steady state creep of solder can be expressed by a relationship of the form [10-12] dεs dt = Css[sinh(ασ)] n exp( -Qa kT ) (1) where dεs/dt is the steady state strain rate, k is Boltzmann's constant, T is the absolute temperature, σ is the applied stress, Qa is the apparent activation energy, n is the stress exponent, α prescribes the stress level at which the power law dependence breaks down, and Css is a constant. Steady state creep data for 62Sn36Pb2Ag solder joints is shown in Figure 2.

Fatigue crack propagation behaviour derived from S–N data in very high cycle regime

Abstract: The crack propagation law was derived from the S-N data in the very high cycle fatigue of a bearing steel. The propagation rate, da/dN (m/cycle), of surface cracks was estimated to be a power function of the stress intensity range, ΔK (MPa√m) with the coefficient C s = 5.87 x 10- 13 and the exponent m s = 4.78. The threshold stress intensity range was 2.6MPa√m. The crack propagation from internal inclusions was divided into Stages I and II. For Stage I, the coefficient of the power law was C o = 3.44 x 10 -21 and the exponent m o = 14.2. The transition from Stage I to II took place at ΔK = 4.0 MPa√m. For Stage II, the coefficient was C i = 2.08 x 10 -14 and the exponent m i = 4.78. The specimen size and loading mode did not influence the surface fatigue life, while the internal fatigue life was shortened in larger specimens and under tension-compression loading. For ground specimens, the surface fatigue life was raised by the compressive residual stress, while reduced by the surface roughness introduced by grinding. For shot-peened specimens, fatigue fracture did not take place from the surface because of a high surface compressive residual stress. The internal fatigue life was reduced by the tensile residual stress existing in the interior of the specimens.

An orthotropic damage model for masonry structures

Abstract: An orthotropic damage model specifically developed for the analysis of brittle masonry subjected to in-plane loading is described. Four independent internal damage parameters, one in compression and one in tension for each of the two natural axes of the masonry, are defined allowing the stiffness recovery at crack closure as well as the different inelastic behaviour along each natural axis to be considered. The damage field of the material is defined in terms of four equivalent stresses and results, in the space of the in-plane effective stresses, in a double pyramid with a rectangular base where the slopes of the faces correspond to the internal friction angle of the material. The equivalent stresses also control the growth of the damage parameters. The returning path from the effective to the damaged stresses is given by multiplication by a fourth-rank damage effect tensor, which is a function of the damage parameters and of the effective stress state. Mesh size regularization is achieved by means of an enhanced local method taking into account the finite element size. Good agreement has been found in the comparison between numerical results and experimental data both for masonry shear panels and for a large-scale masonry holed wall. Copyright © 2002 John Wiley & Sons, Ltd.

A new criterion for the prediction of crack development in multiaxially loaded structures

Abstract: In many cases the lifetime of technical structures and components is depending on the behaviour of cracks. Due to the complex geometry and loading situation in real-world structures cracks are often subjected to a superposition of normal, in-plane and out-of-plane loading. In this paper a new criterion for 3D crack growth under multiaxial loading, that means superposition of the fracture modes Mode I, II and III, is described. The criterion allows the prediction of three-dimensional crack surfaces advancing from arbitrary 3D crack fronts with the help of the two deflection angles φ0 and ψ0. The underlying theory for the development of this new criterion is described in detail.

Very high‐cycle fatigue behaviour of shot‐peened high‐carbon–chromium bearing steel

Abstract: Effect of shot-peening on fatigue behaviour in the gigacycle regime was investigated in order to clarify the duplex S-N curve characteristics. Cantilever-type rotary bending fatigue tests were performed in laboratory air at room temperature by using hourglassshaped specimens of high-carbon-chromium bearing steel, JIS SUJ2. Fatigue crack initiation site changed from the surface of untreated specimen to the subsurface of the specimen because of hardening and compressive residual stress with shot-peening in the region of high-stress amplitude. On the other hand, no difference in fatigue life controlled by the subsurface crack initiation between untreated specimen and shot-peening one was observed in high-cycle region. It was suggested that the S-N curve corresponding to the internal fracture mode is inherent in the material, as compared with the S-N curve of surface fracture mode, which is affected by surface conditions, environmental conditions and so on. Subsurface crack initiation and propagation behaviour were discussed under the detailed measurement of crack initiation area and shape of the fish-eye fracture surface.

Stress-Induced Crystallization around a Crack Tip in Natural Rubber

Abstract: Stress-induced crystallization, orientation, and crystallinity have been measured by X-ray diffraction around cracks in a cis-1,4-polyisoprene sample drawn at low ratio, λ < 3.5. A zone of maximum crystallinity and a transition zone of varying crystallinity are observed; the dimensions of these semicrystalline zones surrounding the crack tip are measured as a function of the draw ratio, crack length, and cross-link density. An isocrystallinity map is established; this permits one to measure the local draw ratio and then the local stress around the crack tip. The stress distribution around the crack tip is compared with the scaling laws predicted by the linear or nonlinear elasticity theories. Finally, one shows the existence of a relaxed zone between the crack tip, the crack surface, and the lateral sides of the sample. The surface of this zone is comparable to the area of the semicrystalline zone around the crack tip and to the crack opening surface.

Fretting fatigue crack initiation mechanism in Ti–6Al–4V

Abstract: r Fretting fatigue crack initiation in titanium alloy, Ti-6Al-4V, was investigated experimentally and analytically by using finite element analysis (FEA). Various types of fretting pads were used in order to determine the effects of contact geometries. Crack initiation location and crack angle orientation along the contact surface were determined by using microscopy. Finite element analysis was used in order to obtain stress state for the experimental conditions used during fretting fatigue tests. These were then used in order to investigate several critical plane based multiaxial fatigue parameters. These parameters were evaluated based on their ability to predict crack initiation location, crack orientation angle along the contact surface and the number of cycles to fretting fatigue crack initiation independent of geometry of fretting pad. These predictions were compared with their experimental counterparts in order to characterize the role of normal and shear stresses on fretting fatigue crack initiation. From these comparisons, fretting fatigue crack initiation mechanism in the tested titanium alloy appears to be governed by shear stress on the critical plane. However, normal stress on the critical plane also seems to play a role in fretting fatigue life. At present, the individual contributions/importance of shear and normal stresses in the crack initiation appears to be unclear; however, it is clear that any critical plane describing fretting fatigue crack initiation behaviour independent of geometry needs to include components of both shear and normal stresses.

Numerical investigation of residual stress fields and crack behavior in TBC systems

Abstract: Due to thermal expansion mismatch and bond coat (BC) oxidation, high residual stresses are induced in the thermal barrier coating (TBC), leading to failure by spalling and delamination. Using the finite element method (FEM), an analysis of the stress distributions in TBC systems, which is a prerequisite for the understanding of failure mechanisms, was performed. As cracking usually occurs at or near the interfaces between BC/thermally grown oxide (TGO) and TBC/TGO depending on the processing mode of the TBC, cracks in the interface region were considered in the FE models in order to determine the loading conditions for their propagation and, thus, the failure criteria of the TBCs. Due to the mode mixity of these cracks, suitable methods are required for the determination of the fracture mechanics parameters needed for their assessment, such as the strain energy release rate G. The modified crack closure integral method (MCCI) was found to be a very efficient tool which can be combined easily with an FE analysis and leads to highly accurate energy release rate values. Moreover, this method enables the determination of mode-dependent energy release rates. Using this tool and appropriate crack propagation criteria, TBC failure models could be developed and verified.

Analog experiments on magma-filled cracks: Competition between external stresses and internal pressure

Abstract: We have performed two series of analog experiments using gelatin to study the propagation of liquid-filled cracks in stressed medium. The first series was designed to study the competition between the external stress and the liquid excess pressure in controlling the propagation direction. We systematically controlled the external stress and the liquid excess pressure by changing the surface load and the liquid volume. An ascending crack progressively deflected to be perpendicular to the maximum tensile direction of the external stress. The degree of deflection depends on the ratio of the shear stress on a crack plane to the average liquid excess pressure. More deflection was observed for a crack with a larger ratio. No significant deflection was observed for the ratio less than 0.2. The volcanic activity in a compressional stress field might be understood in the context of this competition. The first series also demonstrated the importance of the gradient of the crack normal stress as a driving force for propagation. The vertical gradient of the gravitational stress generated by a mountain load can control the emplacement depth of magmas, and it might lead to the evolution of eruption style during the lifetime of a volcano. The second series was designed to study the three-dimensional interaction of two parallel buoyancy-driven cracks. The deflection of the second crack takes place, when the ratio of the shear stress generated by the first one to the average excess pressure of the second crack is larger than 0.2. If the second crack reaches the first one, the interaction can lead to the coalescence of two cracks. It has directivity: the region of coalescence extends more in the direction perpendicular to the first crack than in the direction parallel to it. It reflects the stress field around the first crack. This directivity might cause a characteristic spatial variation of magma chemistry through magma mixing.

Computational model for analysis of bending fatigue in gears

Abstract: A computational model for determination of service life of gears in regard to bending fatigue in a gear tooth root is presented. The fatigue process leading to tooth breakage is divided into crack initiation (Ni) and crack propagation (Np) period, where the complete service life is defined as N=Ni+Np . The strain-life method in the framework of the FEM method has been used to determine the number of stress cycles Ni required for the fatigue crack initiation. Gear tooth crack propagation was simulated using a FEM method based computer program which uses principles of linear elastic fracture mechanics. Paris equation is then used for the further simulation of the fatigue crack growth. The presented model is used for determination of service life of real spur gear made from through-hardened steel 42CrMo4.

Micromechanical approach to nonlinear poroelasticity: application to cracked rocks

Abstract: This paper considers a saturated porous medium in which the matrix is a cracked solid. Progressive crack closure is responsible for an overall nonlinear poroelastic behavior. The state equations of nonlinear poroelasticity are derived in a differential form within a micromechanical framework. When a hydraulic connection exists between the cracks and the pores of the porous space, the tangent drained stiffness tensor as well as the tangent Biot tensor and modulus are shown to depend on Terzaghi effective stress. Estimates for these coefficients as functions of Terzaghi effective stress are then derived with the tools of homogenization for disordered media. They are based on a crack closure criterion giving the condition for a crack to be closed under a given macroscopic stress state, depending on its aspect ratio. In the case of an isotropic orientation of cracks, it is shown that the influence of cracks on the overall poroelastic properties is governed by the crack density parameter which characterizes the distribution of aspect ratios. Conversely, an experimental methodology for the determination of the distribution of aspect ratios from the measurement of the macroscopic compliance is proposed.