Mechanical Stress Intensity Factors Research Articles

A new semi-analytic method for calculating the thermal–mechanical coupling stress intensity factor of interfacial crack

The interfacial crack thermal–mechanical coupling stress intensity factor (SIF) calculation plays an important role in anti-cracking design and safety assessment of compressed air energy storage (CAES) multi-layer cavern. In current SIF calculation method, there is no consideration of thermal–mechanical coupling effect caused by the difference between the singularity of stress field (λ) and temperature field (λT). In this study, a new semi-analytic method for calculating the thermal–mechanical coupling SIF of interfacial crack is established based on a new thermal–mechanical coupling Williams expansion for the cases of both insulated and constant temperature. The singularity index of temperature field at the crack-tip is dependent on the material parameters (heat conduction coefficient ki) for the crack perpendicular to and terminated at the interface, but independent on the material parameters (ki) for the crack located at the interface. The larger the difference of bi-material's heat conduction coefficient (ki), the larger the value of stress field when the crack is located on the side of larger Young's modulus (Ei) or on the side of lower ki. The semi-analytic method is degenerately verified by available literature results (without thermal–mechanical coupling term) and completely verified by finite element results (with thermal–mechanical coupling term), which can provide a theoretical basis for anti-cracking optimal design of CAES multi-layer caverns under thermal–mechanical loading condition.

Interfacial Fracture Caused by Electromigration at Copper Interconnects

Abstract The present investigation delves into the failure model of cracking at the Cu/dielectric interface, specifically at the anode end of a copper interconnect that is triggered by electromigration. The study employs the continuous dislocation model to determine the stress field caused by interfacial mass diffusion that exists within and outside of the copper line. Apart from the anticipated tensile or compressive stress on the cathode or anode side, an anomalous stress singularity is identified at the interface between the dielectric layer and the anode end of the copper line. This singular stress distribution leads to cracking in the compressive portion of the dielectric layer at the anode end under the influence of electromigration. The theoretical predictions are in good agreement with experimental data, and a novel failure criterion akin to the stress intensity factor in fracture mechanics is formulated.

Numerical Analysis of Fracture Behaviour for Cracked Joints in Corrugated Plate Girders Repaired by Stop-Holes.

The efficient crack eliminated stop-hole measure was proposed to repair and reduce the stress concentration associated fracture risk of the corrugated plate girders by setting it at the critical joint of flange plate with tightened bolts and gaskets under preloading. To investigate the fracture behaviour of these repaired girders, parametric finite element analysis was conducted, focusing on the mechanical feature and stress intensity factor of crack stop-hole in this paper. The numerical model was verified against experimental results first, and then the stress characteristics due to the presence of crack open-hole were analysed. It was found that the moderate-sized open-hole was more effective than the over-sized open-hole in the reduction of stress concentration. For the model with prestressed crack stop-hole through bolt preloading, the stress concentration was nearly 50% with the prestress around open-hole increased to 46 MPa, but such a reduction is inconspicuous for even higher prestress. Relatively high circumferential stress gradients and the crack open angle of oversized crack stop-holes were decreased owing to additional prestress effects from the gasket. Finally, the shift from the original tensile area around the edge of the crack open-hole that was prone to fatigue cracking to a compression-oriented area is beneficial for the reduction of stress intensity factor of the prestressed crack stop-holes. It was also demonstrated that the enlargement of crack open-hole has limited influence on the reduction of stress intensity factor and crack propagation. In contrast, higher bolt prestress was more beneficial in consistently reducing the stress intensity factor of the model with the crack open-hole, even containing long crack.

Influence of Form Defect on the Mechanical Behavior and Stress Intensity Factor of Shrink-Fitted Thick-Walled Cylinders

In this research work, the finite element software, ABAQUS is used to study by simulations the influence of form defect on mechanical behavior of a shrink-fitted assembly presenting internal radial cracks. Under the action of contact pressure induced by the tightening between two cylinders, these cracks resulting from incorrect assembly operations or materials elaboration defect, can be harmful to the assembly. Various simulations were carried out in two modeling cases, taking into account the geometric parameters of defect (amplitude Df), of cylinders (thickness t) and of cracks (length a, ratio a/t). Another important parameter such as the tightening was also considered in the modeling. The first modeling relates to the case with defect, external cylinder presents an oval (elliptical) form defect and internal radial cracks. The other concerns the perfect equivalent case (without form defect). The comparison of results obtained by two models shows that form defect modifies the uniformity of equivalent stresses distribution in cylinders and increases the value of stress intensity factor (SIF) KI in cracks. Defect amplitude and tightening significantly influence the value of equivalent stress and that of stress intensity factor (SIF) <i>KI</i>.

A novel strong-form random differential quadrature method to compute the stress intensity factor in fracture mechanics

A strong-form based meshless random differential quadrature (RDQ) method is extended in a novel manner to fracture problems for computing the stress intensity factors (SIF), and called as extended-RDQ method (ExRDQM). The applicability of ExRDQM is successfully demonstrated in SIF computation of the single edge notched, double edge notched, and central cracked specimens under the mode-I and mode-II loading conditions. The ExRDQM consist of fixed-reproducing kernel particle method (fixed-RKPM) coupled with the local differential quadrature (LDQ) method and a novel strain computation approach (required due to uniformly or randomly distributed field nodes) combined with the correct boundary conditions specifically required by strong-form based numerical methods. The ExRDQM does not require: (1) nodal connectivity information for the shape function computation, (2) re-meshing (h-refinement), or (3) basis function enrichment, making it one of the alternatives to weak-form based methods (e.g. element free Galerkin method) and extended finite element method.The SIF in ExRDQM is numerically computed by: (1) displacement field interpolation method around the crack tip, and (2) modified crack closure integral method, and the results are compared with both the finite element solutions (ABAQUS) and analytical near-field expressions. The presented results show that the proposed methodology is efficient, accurate, and reasonably reliable while modelling the fracture problems, and it can very well be extended for the crack propagation in a near future.

Dynamic Mechanical Response, Cracking Behavior, and Stress Intensity Factors of Cement Mortar Specimens with Open and Closed Flaws

Major civil and military infrastructures are usually located in mountainous areas with complex geological structures. When subjected to impact loads caused by operational blasting or seismic activities, the inherent flaws or joints in the hosting rock mass may grow irreversibly and eventually and cause the entire structure to collapse. It is, therefore, desirable to understand the mechanical and cracking behaviors of flawed rock structures under dynamic loads. In this work, the cement mortar is used to make the plate specimens, and two different types of flaws, i.e., the open and the closed (resin-filled) flaws, with different inclination angles from 0° to 90° with respect to the loading direction are prefabricated. The nominal strength, crack initiation, and failure characteristics of the specimens under different loading rates are investigated using the split Hopkinson bar (SHPB) system in conjunction with the digital image correlation (DIC) technique. The results indicate that the dynamic nominal strength of both two types of specimens shows similar loading rate and flaw angle dependency, specifically, monotonically increasing with the increase of the loading rate while increasing first and then decreasing with increasing the flaw inclination angle. The strength of specimens with an open flaw is obviously lower than that of the specimens with a closed flaw at a similar loading rate. Besides, the failure mode of specimens with an open flaw is mainly an X-shaped tensile or tensile-shear mixed form regardless of the flaw inclination, whereas the resin-filled flawed specimens always fail in the form of an atypical X-shaped shear pattern with obvious randomness. Moreover, the stress field around the crack tip is carefully extracted based on the obtained displacement field from DIC analysis; the stress intensity factors at crack initiation onset also show flaw inclination- and loading rate-dependent behavior. The strength, cracking behavior, and stress field around the tip during the dynamic loading are closely related to the friction effect between the flaw surfaces. The findings in this work provide some basic insights into the cracking mechanism of rock with open and closed flaws under dynamic loading conditions.

Qualification of uniform fatigue damage tolerance law for additively manufactured and cast Al-Si alloys

The demand on lightweight structures and materials are steadily growing in automotive and aerospace industries. Hypo-eutectic Al-Si alloys are promising candidates due to its high specific material strength and corrosion resistance. Near net shape manufacturing by additive manufacturing (AM) or castings allow a high resource efficiency. The complex geometries lead to a wide range of structural features due to process-induced variations in local cooling rate. Therefore, the relationships between structural characteristics (e.g. dendrites, grain, eutectic, porosity, lack of fusion) and fatigue behavior have to be understood to enable a lightweight and reliable design of Al-Si alloys. In this study, the effect of process and process-induced structural characteristics on stress-strain behavior (quasi-static, cyclic) and high cycle fatigue behavior were characterized. The specimens were processed by laser-based powder bed fusion (PBF-LB) and sand casting (SC) with variation in porosity and dendrite arm spacing. Hereby, the age-hardenable Al-Si alloys AlSi10Mg (AM, SC) and AlSi7Mg (SC) were investigated. AM batches were tested in as-built condition. All casting batches got a HIP densification and T6 heat treatment. The fatigue results were analyzed based on nominal stresses according to Woehler (S-N curve) and local stress intensity based on linear-elastic fracture mechanics (stress intensity factor) as well as elastic-plastic fracture mechanics (J integral). J integral based Shiozawa diagrams allowed a sufficient and uniform fatigue damage tolerance (FDT) assessment for all AM and SC alloys. Hereby, the FDT of Al-Si alloys were dominated by defects (size, position) and cyclic stress-strain behavior (yield strength, cyclic hardening).

Diverter damper force analysis and stress intensity factors for its double fillet welds by boundary element method

Mechanisms usually transmit power by welded links into a shaft. Should this weld be partial, like fillet welds, there will be an area of stress concentration that could behave like a crack due to sharp corners. These can lead to structural failures due to fatigue. Consequently, to properly design, inspect and maintain these mechanisms it is necessary to use fracture mechanics stress intensity factors. The crack mesh simplicity required by the boundary element method allows easy modeling even for complex geometry. This technique will be used to obtain such parameters for a double fillet weld found in a diverter damper mechanism responsible for controlling hot gas flow to heat recovery steam generator in power plants. But the solutions presented can be used for similar geometrical configurations, specially to shaft link mechanisms. Empirical equations were also obtained to further ease fracture mechanics and fatigue analysis for this kind of geometry.

Estimation of the service load capacity of plain concrete arch bridges using a novel approach: Stress intensity factor

Masonry arch bridges have furnished railway networks as important infrastructures. The evaluation of the behavior of masonry arch bridges has drawn a great deal of attention over the past years due to the increase in the speed of railway fleet, need for augmentation of trains axle loads, and increase in the number of vehicles. These critical structures have been designed for service loads demanded at past times and since service loads are different in the present time, their behavior crucially needs to be assessed. Various analytical, experimental, approximate, and numerical methods have been proposed so far to estimate the residual capacity of masonry arch bridges. The present paper aims to predict the maximum service load of railway plain concrete arch bridges using a new approach with the aid of stress intensity factor in the fracture mechanics. Since stress intensity factor is solved analytically only for highly simple problems, a numerical approach and the finite element method were used in the present paper to calculate this parameter. Finally, given the stress intensity factor and proposing a relation for concrete toughness based on a statistical study, the maximum service load of these vital structures is obtained. To validate the results, two plain concrete arch bridges —located at kilometer 23 and 24 of Tehran-Qom Old Railway— were used. The results revealed that the proposed method has agreed well with the field observations.

Automatic prediction of the fatigue crack trajectory in plane finite element models

A module for automatic prediction of the fatigue crack trajectory in plane finite-element models in Ansys APDL software package was developed. Crack propagation is modeled by exclusion of elements from the active set in the direction, which is determined based on criterion of the maximum energy flux to the crack tip. The module determines the parameters of fracture mechanics (stress intensity factor and J-integral) at each step of crack propagation.

Mixed mode interface fracture toughness of a multi-directional composite – UD/woven pair

Twenty-seven mixed mode Brazilian disk specimens were tested to obtain the fracture toughness of a delamination between two fiber reinforced composite plies in a multi-directional laminate, manufactured by means of a wet-layup. Using finite element analyses and conservative integrals, mechanical and residual curing stress intensity factors were found and used to calculate the interface energy release rate and phase angles. Based on these results, a three-dimensional failure criterion is proposed to obtain a failure surface. This criterion may be used to predict failure of a structure containing this material and interface.

Thermo-mechanical shock fracture analysis by meshless method

Different types of mechanical and thermal shock loads are considered to investigate transient stress intensity factors of two/three dimensional cracked specimens via meshless method with linear test function. Steady state and transient analyses show that the method is reliable. The effect of crack length, density and Lord-Shulman relaxation time on stress intensity factors are studied. Results represent the different effect of crack length on mechanical and thermal stress intensity factors. Various theoretical and real values of relaxation time are used to show how thermal stress intensity factor curves change when modified Fourier heat conduction law is employed compared with classical Fourier law. Additionally, the effect of specimen size on non-Fourier thermal stress intensity factor curves is investigated. We observed that using a functionally graded material instead of a composite coated substrate reduces local mean and peak values of transient thermal stress intensity factors.

Nearly Mode I Fracture Toughness and Fatigue Delamination Propagation in a Multidirectional Laminate Fabricated by a Wet-Layup

Five double cantilever beam specimens were tested quasi-statically to obtain a GIR resistance curve. In addition, nine double cantilever beam specimens were tested in fatigue to obtain a Paris-type relation to describe the delamination propagation rate da/dN where a is delamination length and N is the cycle number. Displacement ratios of Rd = 0.10 and 0.48 were used for five and four specimens, respectively. The specimens were fabricated by means of a wet-layup process from carbon fiber reinforced polymer plies. The interface containing the delamination was between a unidirectional fabric and a woven ply. The fracture toughness and fatigue delamination propagation protocols are outlined. The mechanical and thermal residual stress intensity factors were obtained by means of finite element analyses and the conservative M-integral along the delamination front. They were superposed to determine the total stress intensity factors. It was found that the total mode I stress intensity factor dominates the other two stress intensity factors. Thus, nearly mode I deformation was achieved. Interpolation expressions for the mechanical and thermal residual stress intensity factors were determined using three and two-dimensional fittings, respectively. Results are presented with an expression for GIR determined. Moreover, the fatigue data is described including threshold values and master-curves. These results shed light on the behavior of delamination propagation in multidirectional laminate composites.

Fatigue crack growth in bending: Successful correlation of mean stress (stress ratio) effects using the change in net‐section strain energy

AbstractA physically based correlation of mean stress (or stress ratio) effects, during fatigue crack growth in bending, is demonstrated using the concept of the change in net‐section cyclic strain energy. This study extends the net‐section approach, which was successfully demonstrated previously for middle‐cracked tension specimens, here to bending. A straightforward analytical derivation of the change in net‐section cyclic strain energy is shown using the mechanics of beam bending. Using experimental data, it is shown that the change in net‐section cyclic strain energy successfully correlates the effect of mean stress on fatigue crack growth rates for a steel, an aluminium alloy, a titanium alloy, and a WC‐Co cermet. It is also shown that the net‐section‐based stress intensity factor, morphed from the change in net‐section strain energy, agrees excellently with the fracture mechanics‐based stress intensity factor. This is to show that the proposed net‐section‐centric fracture mechanics approach for fatigue is physical and that the origin of fracture mechanics stress intensity factor appears to be actually rooted in the change in the net‐section strain energy. Hence, the net‐section‐centric approach appears to be superior to the crack‐centric conventional fracture mechanics approach, and a physical treatment of the fatigue crack growth behaviour appears to be possible.

Prediction of fatigue life by crack growth analysis

This work proposes an improved mechanical driving force parameter for crack growth analysis. The proposed parameter investigates fatigue crack growth FCG under constant amplitude loading, considering the influence of residual stress distribution near the crack tip. A 2D FE Analysis is developed in order to compute the stress distribution in the vicinity of the crack tip with in the framework of elastic-plastic fracture mechanics (EPFM). Elastic stress intensity factors are computed using both analytical solution and the extended finite element method (XFEM). Residual stress intensity factors are determined using the weight function through numerical analysis. The authors estimate the residual fatigue crack growth life of 7075-T6 Aluminum alloy attachment lugs with single through-thickness crack under various loading conditions. Moreover, a comparison with the available experimental data is performed. It is proved that this improved mechanical parameter so-called residual-corrected stress intensity factor can better predict fatigue life with a greater accuracy compared with experimental results.

Torsion analysis of cracked circular bars actuated by a piezoelectric coating

This study presents a formulation for a bar with circular cross-section, coated by a piezoelectric layer and subjected to Saint-Venant torsion loading. The bar is weakened by a Volterra-type screw dislocation. First, with aid of the finite Fourier transform, the stress fields in the circular bar and the piezoelectric layer are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations. Numerical results are discussed, to reveal the effect of the piezoelectric layer on the reduction of the mechanical stress intensity factor in the bar.

3D explicit-BEM fracture analysis for materials with anisotropic multifield coupling

An explicit and unified boundary element formulation for the linear fracture analysis of three-dimensional bodies with general anisotropic multifield coupling is presented. The herein considered multifield media include, as particular cases, the purely elastic, piezo-electric and magneto-electro-elastic material models. The proposed formulation is based on the fundamental solutions for displacements and tractions recently introduced by Buroni and Sáez (2010), which presents the remarkable features of being exact, explicit in terms of the Stroh’s eigenvalues and valid for mathematically degenerate as well as non-degenerate materials. Behaviour around the crack front is modeled with quarter-point elements for the extended displacements (elastic displacements, electric potential and magnetic potential) and singular quarter-point elements for the extended stresses (mechanical stresses, electric displacements and magnetic inductions) which allow for the direct extrapolation of the extended stress intensity factors (the mechanical stress intensity factors in the three classical modes KI, KII and KIII, the electric displacement intensity factor KIV and the magnetic induction intensity factor KV) from the computed nodal values at the singular quarter-point elements. Some benchmark examples are presented and discussed in order to validate this simple and robust approach for the assessment of multifield fracture parameters.

Natural frequency changes due to damage in composite beams

Transversal cracks in structures affect their stiffness as well as the natural frequency values. This paper presents a research performed to find the way how frequencies of sandwich beams change by the occurrence of damage. The influence of the locally stored energy, for ten transverse vibration modes, on the frequency shifts is derived from a study regarding the effect of stiffness decrease, realized by means of the finite element analysis. The relation between the local value of the bending moment and the frequency drop is exemplified by a concrete case. It is demonstrated that a reference curve representing the damage severity exists whence any frequency shift is derivable in respect to damage depth and location. This curve is obtained, for isotropic and multi-layer beams as well, from the stored energy (i.e. stiffness decrease), and is similar to that attained using the stress intensity factor in fracture mechanics. Also, it is proved that, for a given crack, irrespective to its depth, the frequency drop ratio of any two transverse modes is similar. This permitted separating the effect of damage location from that of its severity and to define a Damage Location Indicator as a sequence of squared of the normalized mode shape curvatures.

Elliptical and circular bonded composite repair under mechanical and thermal loading in aircraft structures

In this study, the three-dimensional finite element method is used to achieve a comparison between the semi circular and semi elliptical patch repairs in aircraft structures. The comparison was done by the analysis of : the mechanical and thermal stress intensity factors (SIF and TSIF) at the tip of repaired crack and the distribution of the adhesive stresses for the two patch shapes. The obtained results show that the semi circular shape of the patch presents lower stress intensity factor at the crack tip, which is beneficial for the fatigue life and lower adhesives stresses, which is beneficial for the repair durability. In addition the circular patch is subjected to less significant thermal residual stresses compared to the elliptical shapes.

Influence of inclined electric fields on the effective fracture toughness of piezoelectric ceramics

Electric fields effectuate the fracture behavior of ferroelectrics on different scales. On the atomic scale, forces in covalent bonds are influenced. On the mesoscopic scale, the ferroelectric domain wall motion shields the crack tip or leads to an additional loading. Based on classical approaches, on the macroscopic scale, the electric field has a major impact on the energy release rate and the electric displacement intensity factor; however, it scarcely influences the mechanical stress intensity factors. The situation is different if Maxwell stresses at crack faces, as a consequence of the jump of dielectric properties, are incorporated in the crack tip loading analysis. First, general considerations deal with the question how a fracture criterion has to be formulated, incorporating all three scales. On the macroscopic scale, the influence of an arbitrarily inclined electric field on the critical mechanical crack loading is investigated. The extended model, in particular, reveals the significance of electric fields parallel to the crack faces. A combined analytical–numerical approach is applied to solve the coupled two-domains problem of solid and crack dielectric, supporting the well-established capacitor approach even for inclined electric fields.