Pseudo plane stress mode II crack growth in plastic materials

The near tip field of mode II crack that grows in thin bodies with power hardening or perfectly plastic behavior is analyzed. It is shown that for power hardening behavior, the pseudo plane stress field possesses the logarithm singularity, i.e. σ (ln r)²/(n−1), (ln r)^{2n/(n − 1)}, where r is the distance from the crack tip, n the hardening exponent is σⁿ. When n → ∞ the solution reduced to that for the perfectly plastic case.     

Experimental quantification of the plastic blunting process for stage II fatigue crack growth in one-phase metallic materials

The plastic blunting process during stage II fatigue crack growth was studied in pure polycrystalline Ni to investigate effects of strain localization and inelastic behavior on the kinematics of crack advance. Correlations were obtained between strain fields ahead of a fatigue crack, crack advance per cycle and crack growth kinetics. Strain fields were quantified using a combination of in situ loading experiments, scanning electron microscopy and digital image correlation for 8 < ΔK < 20 MPa m^1/2 and a fixed load ratio of 0.1. Results indicate that strain localized along a dominant deformation band, which was usually crystallographic and carried mostly pure shear for large loads and was of mixed character for lower loads. Instances of double deformation bands were observed, with bands acting either in a simultaneous or alternating fashion. It was found that the area integral of the opening strain for values larger than a given threshold, an “integrated” strain, had a power-law relationship with ΔK, with the exponent approximately equal to the Paris exponent (m). Therefore, the crack growth rate was proportional to the integrated strain. An analysis based on this correlation and the presence of dominant shear bands indicated that the integrated strain is related to the accumulated displacement in the band. This, in turn, is proportional to the product of the cyclic plastic zone radius and the average shear strain ahead of the tip, which represents a basic length scale for plastic blunting. Assumptions on the load dependence of these quantities, based on their observed spatial variation, allowed estimating $m=2\left(1+\frac{1}{1+n^{\prime }}\right)$, where n′ is the cyclic hardening exponent (0 < n′ < 1). This gives 3 < m < 4, which accounts for about 50% of the observed values of m between 1.5 and 6 for a wide variety of metallic materials.     

Driving forces and kinking of an oblique crack in bonded nonhomogeneous materials

Summary  Plane elasticity solutions are presented for the problem of an oblique crack in two bonded media. The material model under consideration consists of a homogeneous half-plane with an arbitrarily oriented crack and a nonhomogeneous half-plane. The Fourier integral transform method is employed in conjunction with the coordinate transformations of field variables in the basic elasticity equations. Formulation of the crack problem results in having to solve a system of singular integral equations for arbitrary crack surface tractions. A crack perpendicular to or along the bonded interface between the homogeneous and nonhomogeneous constituents arises as a limiting case. In the numerical results, the values of mixed-mode stress intensity factors are provided for various combinations of relevant geometric and material parameters of the bonded media. Subsequently, the infinitesimal kinks from the tips of a main crack are presumed, with the corresponding local driving forces being evaluated in terms of the stress intensities of the main crack. The criterion of maximum energy release rate is applied with the aim of making some conjectures concerning the likelihood of kinking and the probable kink direction based on the approximation of local homogeneity and brittleness of the crack-tip behavior. Received 25 September 2001; accepted for publication 13 February 2002     

A semi-infinite interface crack interacting with subinterface matrix cracks in dissimilar anisotropic materials. II. Numerical results and discussion

Based on the investigation performed in Part I of this series, numerical results for the interaction between a semi-infinite interface crack and multiple subinterface matrix microcracks in three kinds of material combinations are given in Part II. The major interaction behaviors are discussed in detail. Special attention is focused on the influences of the different material combinations, the T-stress, the orientation angles, and the location angles of the microcracks on the local stress intensity factor at the interface crack tip. In addition, the variable tendencies of the interaction effect induced from change of the distance between the interface crack tip and the centers of the microcracks are studied. It is concluded that the different material combinations introduced in this paper have little influence on the variable tendencies of the effect, but have significant influence on the effect in magnitude. Detailed comparisons of the results with those in a homogeneous orthotropic material show that the dissimilar materials shift the maximum amplification angle, the maximum shielding angle, the neutral shielding angle, and the neutral T-stress angle, respectively.     

An interaction energy integral method for nonhomogeneous materials with interfaces under thermal loading

A plane crack problem of nonhomogeneous materials with interfaces subjected to static thermal loading is investigated. A modified interaction energy integral method (IEIM) is developed to obtain the mixed-mode thermal stress intensity factors (TSIFs). Compared with the previous IEIM, the original point of this paper is: the domain-independence of the modified IEIM still stands in nonhomogeneous materials with interfaces under thermal loading. Therefore, the modified IEIM can still be applied to obtain the TSIFs of nonhomogeneous material even if the integral domain includes interfaces. The modified IEIM is combined with the extended finite element method (XFEM) to solve several thermal fracture problems of nonhomogeneous materials. Good agreement can be obtained compared with the analytic solutions and the domain-independence of the IEIM is verified. Therefore, the present method is effective to study the TSIFs of nonhomogeneous materials even when the materials contain interfaces. The influence of the discontinuity of the material properties (thermal expansion coefficient, thermal conductivity and Young’s modulus) on the TSIFs is investigated. The results show that the discontinuity of both thermal expansion coefficient and Young’s modulus affects the TSIFs greatly, while the discontinuity of thermal conductivity does not arouse obvious change of the TSIFs.     

A crack in functionally gradient materials under thermal shock

Summary This paper deals with the problem of two bonded semi-infinite functionally gradient material plates with a crack at the interface under thermal shock loading conditions. All material properties are supposed to be exponentially dependent on the distance from the crack line. By using both the Laplace transform and the Fourier transform, the problem is reduced to a singular integral equation which is solved numerically. The stress intensity factor versus time for various material constants is calculated. The results show that by selecting the material constants appropriately, the stress intensity factor can be lowered substantially.

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Ein Riß im Funktionalgradientenmaterial unter einem thermischen Schock

Übersicht Die Arbeit behandelt das Problem zweier beschichteter Platten aus einem Funktionalgradientenmaterial mit einem Riß entlang der Verbindungsfläche unter einer thermischen Schockbeanspruchung. Die Materialeigenschaften hängen exponentiell vom Abstand von der Bruchlinie ab. Durch kombinierte Anwendung der Laplace- und der Fourier-Transformation wird das Problem auf eine singuläre Integralgleichung reduziert, die numerisch gelöst wird. Daraufhin wird der Spannungsintensitätsfaktor als Funktion der Zeit für mehrere Sätze von Materialkonstanten berechnet. Es zeigt sich, daß der Spannungsintensitätsfaktor durch eine geeignete Wahl der Materialkonstanten beträchtlich reduziert werden kann.

     

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg–Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase-fields. The main challenge addressed here is encoding various electromechanical crack models (introduced as crack-face boundary conditions in sharp models) into the phase-field framework. The proposed models are verified through comparisons with the corresponding sharp-crack models. We also perform two dimensional finite element simulations to demonstrate the effect of the different crack-face conditions, the electromechanical loading and the media filling the crack gap on the crack propagation and the microstructure evolution. Salient features of the results are compared with experiments.     

Subcritical crack growth in strain-hardening materials with allowance for strain anisotropy

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 2, pp. 90–94, February, 1988.     

Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials

Stresses are determined for a finite cylindrical crack that is propagating with a constant velocity in a nonhomogeneous cylindrical elastic layer, sandwiched between an infinite elastic medium and a circular elastic cylinder made from another material. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. An internal gas pressure is then applied to the crack surfaces. The solution is derived by dividing the nonhomogeneous interfacial layer into several homogeneous cylindrical layers with different material properties. The boundary conditions are reduced to two pairs of dual integral equations. These equations are solved by expanding the differences in the crack surface displacements into a series of functions that are equal to zero outside the crack. The Schmidt method is then used to solve for the unknown coefficients in the series. Numerical calculations for the stress intensity factors were performed for speeds and composite material combinations.     

Intergranular and transgranular crack growth at triple junction boundaries in ordered intermetallics

Coincident site-lattice (CSL) and random grain boundaries (GBs) effects on intergranular and transgranular crack propagation paths in ordered intermetallics that are subjected to high rates of strain are investigated. A three dimensional dislocation density based multiple slip crystalline formulation and computational scheme are used for a detailed understanding and accurate characterization of interrelated deformation and failure mechanisms that can occur due to the generation, trapping, interaction, and annihilation of mobile and immobile dislocation densities that are generally associated with finite strain high strain-rate plasticity in L1₂ ordered intermetallics. Results from this study indicate that intergranular crack growth is along the GBs, normal to the stress-axis, and is due to the dominance of normal stresses in the crack-tip region. Transgranular crack growth is along slip-planes, and is due to the dominance of shear stresses in the crack-tip region.     

Fatigue crack growth simulation in coated materials using X-FEM

In the present work, the eXtended Finite Element Method (XFEM) is used to study the effect of bi-material interfaces on fatigue life in galvanised panels. X-FEM and Paris law are implemented in ABAQUS software using Python code. The XFEM method proved to be an adequate method for stress intensity factor computation, and, furthermore, no remeshing is required for crack growth simulations. A study of fatigue crack growth is conducted for several substrate materials, and the influence of the initial crack angle is ascertained. This study also compares the crack growth rate between three types of bi-materials alloys zinc/steel, zinc/aluminium, and zinc/zinc. The interaction between two cracks and fatigue life, in the presence of bi-material interface, is investigated as well.     

Toughness increment by crack growth in toughened structural materials

Material toughening could be furnished by the energy dissipating wakes and bridging segments during crack growth. According to their contributions to the energy integral applicable to a growing crack, the toughening mechanisms are categorized as: dilatational plasticity and induced shear yielding in the crack wakes, bridging due to second inclusion phases, and the matrix bridging caused by wavy crack front. Detailed toughening analysis is pursued for structural polymers and composite materials reinforced by short aligned fibers. Sponsored by the State Education Commission of China and by the Fok Ying-Tung Education Foundation     

Experimental evidence about the controversy concerning Fourier or non-Fourier heat conduction in materials with a nonhomogeneous inner structure

Distinct non-Fourier behavior in terms of finite propagation velocity and a hyperbolic wave like character of heat conduction has been reported for certain materials in several studies published recently. However, there is some doubt concerning these findings. The objective of this paper is to present experimental evidence for a perfectly Fourier-like behavior of heat conduction in those materials with nonhomogeneous inner structure that have been under investigation in the other studies. This controversy needs to be settled in order to understand the physics of heat conduction in these materials.     

Effects of intergrain sliding on crack growth in nanocrystalline materials

Theoretical models are suggested which describe the effects of intergrain sliding on crack growth in nanocrystalline metals and ceramics. Within the models, stress concentration near cracks initiates intergrain sliding which is non-accommodated at low temperatures and effectively accommodated at intermediate temperatures. The first model is focused on the non-accommodated intergrain sliding which leads to generation of dislocations at triple junctions of grain boundaries. These dislocations cause partial stress relaxation in the vicinities of crack tips and thereby hamper crack growth. It is shown that the non-accommodated intergrain sliding increases fracture toughness by 10–30% in nanocrystalline Al, Ni and 3C–SiC. The second model deals with the case of intermediate temperatures. Within this model, intergrain sliding is effectively accommodated by diffusion-controlled climb of grain boundary dislocations. The accommodated intergrain sliding in nanocrystalline materials results in crack blunting which, in its turn, leads to an increase (by a factor ranging from 1.1 to around 3, depending on temperature) of fracture toughness.     

On fatigue crack growth in ductile materials by crack-tip blunting

One of the basic mechanisms for fatigue crack growth in ductile metals is that depending on crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading. In a standard numerical analysis accounting for finite strains it is not possible to follow this process during many cycles, as severe mesh distortion at the crack-tip results from the huge geometry changes developing during the cyclic plastic straining. In the present numerical studies, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 200 full cycles by using remeshing at several stages of the plastic deformation. Three different values of the load ratio R=K_min/K_max are considered. It is shown that the crack-tip opening displacement, CTOD, typically undergoes a transient behaviour, with no crack closure during many cycles, before a steady-state cycling with crack closure at the tip starts to gradually develop.     

Instability of flame in micro-combustor under different external thermal environment

This experiment investigates the performance of a micro-combustor made of a quartz tube. Its surface heat loss is controlled by external wind, the wind temperature ranges from 277 to 1001 K. Compared with the cold wind at 277 K, warm wind at intermediate temperature of 380 K helps stabilize the flame. Because it decreases the surface heat loss, thus inhibits extinction. However, extremely hot wind of 1001 K makes blowout happen easily. The phenomenon is analyzed. The micro-flame retreats to the combustor inlet due to the enhanced heat recirculation at extremely hot wind, which induces insufficient preheating. Subsequently, blowout occurs.     

The effect of load biaxiality on crack growth in non-linear materials

The influence of load biaxiality on the stress field and fracture behavior of a cracked plate is investigated. Considered is a square plate containing a central through the thickness crack and subjected to a biaxial loading perpendicular and parallel to the crack plane. The stress field of the plate is analyzed by a finite element code based on incremental plasticity and the von Mises yield condition. A method based on the strain energy density theory is used to determine the critical stress for crack initiation. It was found that the equi-biaxial loading mode induces the smallest plastic zones, while the critical applied stress for crack initiation becomes maximum. Quite the contrary happens for the shear loading system which causes the largest plastic zones and the minimum applied stress values fro crack growth. Results showing the dependence of the above quantities on the biaxiality of the applied stress are presented in graphical form.