Analysis of dynamic growth of a tensile crack in an elastic-plastic material

The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J₂ flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.     

Brittle fracture dynamics with arbitrary paths. II. Dynamic crack branching under general antiplane loading

The dynamic propagation of a bifurcated crack under antiplane loading is considered. The dependence of the stress intensity factor just after branching is given as a function of the stress intensity factor just before branching, the branching angle and the instantaneous velocity of the crack tip. The jump in the dynamic energy release rate due to the branching process is also computed. Similar to the single crack case, a growth criterion for a branched crack is applied. It is based on the equality between the energy flux into each propagating tip and the surface energy which is added as a result of this propagation. It is shown that the minimum speed of the initial single crack which allows branching is equal to 0.39c, where c is the shear wave speed. At the branching threshold, the corresponding bifurcated cracks start their propagation at a vanishing speed with a branching angle of approximately 40°.     

Automated Control of Stable Crack Growth for R-Curve Measurements in Brittle Materials

Stable crack advance is required for a reliable crack growth resistance (R-Curve) measurement. In bending experiments, manual control of the mechanical load and observation of the growing crack is still being done by the operator. This work presents an approach to partly and fully automated R-curve measurements, where stable crack growth is achieved solely via computer control. The experimental setup in conjunction with an intelligent control algorithm leads to reliable results, even for brittle materials like alumina ceramics, silicon nitride, and glass. Furthermore, it allows for a novel type of measurement, because the device detects any kind of energy release in the specimen, actually also without visible crack extension. The setup has been used successfully for about 3 years. The operating principle is explained and some of the results are presented exemplarily. The method is realized in 4-point-bending, but can be implemented also for other types of specimen and loading to automatically achieve stable crack growth.     

Stress intensity factors for anisotropic layered composites: Part II—isolated double periodic cracks

The formulation in Part I (Theoret. Appl. Fracture Mech. 17, 205–219 (1992)) of this work for collinear cracks in alternate layers of an anisotropic laminate is extended to a system where each of the cracked layer contains a periodic array of parallel cracks. These cracks are also collinear such that they are periodic in two mutually perpendicular directions. Finite Fourier transform is applied at discrete points for one of the space variables reducing the problem to a singular integral equation. The unknown is expressible in terms of the crack opening displacement as in Part I. Displayed graphically are the normalized stress intensity factor, effective stiffness of the laminate, and the interlayer stresses. The local stress intensity factor for the double array crack system is always less than that for a single isolated crack depending on the periodicity ratio. The interlayer stresses directly ahead of the crack are elevated, the intensity of which increases with decreasing distance between the crack tip and interface. Increase in the thickness of the adjoining layer tends to decrease the interlayer stresses nearest to the crack tip, a result that is to be expected.     

Mixed mode fatigue crack growth with a sudden change in loading direction

With a sudden change in the maximum load level, there will be a corresponding change in the crack driving force regardless of whether the load is applied monotonically or cyclically. The effective strain energy density factor range ΔS_p,eff has been used to correlate mixed mode fatigue crack propagation where the crack growth direction is not known as an a priori. Examined in this work is a sudden change of load direction on fatigue crack growth while the load level remains unchanged. Yielding is assumed to be localized near the crack tip such that the crack growth behavior can be described adequately by the elastic stress field. Under the conditions investigated, minimal change on crack growth rates is observed. No firm conclusion could be drawn on deviation of crack path for the case considered.     

Residually Stressed Bimaterial Beam Specimen for Measuring Environmentally Assisted Crack Growth

Background:

Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip.

Objective:

We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading.

Methods:

Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force.

Results:

The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data.

Conclusions:

The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.

     

Effects of surface diffusion and resolved shear stress intensity factor on environmentally assisted cracking

Hydrogen induced crack-tip plastic deformation has been known as the primary mechanism of hydrogen assisted cracking and stress corrosion cracking. It has been systematically shown that the same mechanism of environmentally assisted crack-tip dislocation emission causes hydrogen assisted cracking, stress corrosion cracking, and liquid metal embrittlement cracking.An embrittling chemical species has to reach a crack tip in order to accelerate crack growth. Very close to a sharp crack tip, surface diffusion is shown to be the dominant transport process of embrittling species for stage-II crack growth. The role of surface diffusion in stage II crack growth is analyzed. The constant cracking velocity is proportional to the surface diffusion coefficient of an embrittling species and inversely proportional to a length parameter, , which is related to the transport process upstream.Dislocation emission at a crack tip is driven by crack-tip resolved shear stress. Crack-tip resolved shear stress field is characterized by resolved shear stress intensity factor, K_RSS·K_RSS is defined, the procedure for its calculation outlined, and its applications to crack-tip dislocation emission and environmentally assisted cracking discussed.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

Propagation of a shear crack in a randomly heterogeneous body

Propagation of a crack in a randomly heterogeneous body exposed to longitudinal shear is considered (in a Born approximation). It is proved that the stress means at the crack tip have singularities on the order of (r)^–1/2. The effective coefficient of stress intensity is introduced. It is known that the propagation of a crack in a homogeneous body is of a local nature, i.e., energy consumption in the growth of the crack is completely determined by the coefficient of stress intensity, which is a local characteristic. The equivalence of the force and energy approaches is mathematically expressed by the Irwin equation [1]. An analog of the Irwin equation is obtained for the case of a randomly heterogeneous body.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 145–148, January–February, 1976.     

Fatigue damage in polycrystals – Part 2: Intrinsic scatter of fatigue life

Part 2 deals with the evolution of plastic flow resistance with crack growth from its minimum value (fatigue limit) towards its saturated bulk value (cyclic yield stress). The far-field stress level, the geometry of the crack and the grain size distribution of the material are those parameters that control the area of crack tip plasticity and hence the rate towards saturation. The implication of the far-field stress is held responsible for the violation of the similitude concept and the failure of the stress intensity factor to describe conditions of short cracking. However, an engineering tool based on the stress intensity factor and being able to predict the fatigue life of short cracks can be constructed, considering that the distribution of crack growth rates is intrinsically defined by the material itself. The above allows the development of a set of equations able to construct the fatigue life scatter of the material.     

Fissuration polymodale dans les matériaux viscoélastiques orthotropes

This Note deals with an algorithmic approach about the crack initiation and the crack growth in a viscoelastic media for mixed mode configurations. This numerical model couples a finite element resolution of viscoelastic behavior and the Mθ integral calculus allowing a mixed mode separation in terms of stress intensity factors and energy release rate. The numerical application uses a 2MCG specimen allowing, in the same time, different mixed mode ratios and a crack growth stability. The finite element algorithm allows us to model the crack tip advance by taking into account the crack lip uncohesion in the process zone. It size is defined by taking into account stress field in the crack tip vicinity. To cite this article: R. Moutou Pitti, F. Dubois, C. R. Mecanique 337 (2009).     

Fatigue crack growth induced by domain switching under electromechanical load in ferroelectrics

Reliability calls for a better understanding of the failure of ferroelectric ceramics. The fracture and fatigue of ferroelectric ceramics under an electric field or a combined electric and mechanical loading are investigated. The small-scale domain-switching model is modified to analyze failure due to fracture and fatigue. Effects of anisotropy and electromechanical load coupling are taken into account. Analytical expressions are obtained for domain-switching regions near the crack tip such that of 90° domain switching can be distinguished from 180° domain switching in addition to different initial poling directions. The crack tip stress intensity variation of ferroelectric ceramics due to the domain switching is analyzed. A positive electric field tends to enhance the propagation of an insulating crack perpendicular to the poling direction, while a negative field impedes it. Fatigue crack growth under various coupling loads and effects of the stress field and electric field on near field stress intensity variation are analyzed. Predicted crack growth versus cyclic electric field agrees well with experiment.     

Crack growth under alternating loading

Crack propagation under alternating loading is investigated. Relations between the growth rate of a fatigue defect and loading parameters and the expression for the stress intensity factor are derived for compression of a cracked solid taking into account the possible contact of the crack faces. A model for the deformation of a small region near the crack tip is proposed which allows one to formulate the conditions of residual opening of a growing fatigue crack. The experimental data obtained in tests of steel samples are compared with the results of calculation using the developed procedure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 190–198, September–October, 2008.     

Fatigue crack growth through residual stress fields—theoretical and experimental studies on thick-walled cylinders

Experiments are described which determined the effects of various residual stress distributions on the growth rate of fatigue cracks. For each stress distribution, the contribution (K_RS) to the net stress intensity at the crack tip is determined, and a comparison is then made with the behaviour predicted using a fracture mechanics approach based on a weight function analysis and a simple crack closure model. The example studied is a thickwalled pressure vessel containing a longitudinal crack which grows radially from the inner surface; fatigue cracks were grown under laboratory conditions in ring test specimens. sectioned from vessels which had been cold-expanded by different amounts to increase their pressure limits, and so contained various complex residual stress distributions. The experiments provide direct evidence that the effects of residual stress (and by extension, thermal stress) on the crack tip stress intensity may be modelled conveniently using weight function techniques, and can be incorporated satisfactorily in fatigue crack growth analyses.     

Assessment of creep crack growth due to stress relief

An analysis is conducted to predict stress relief cracking at 550 °C in notched compact tension specimens of Type 316H austenitic stainless steel. The specimens had been subjected to pre-compression to generate a tensile residual stress distribution at the notch tip. This stress distribution is represented by a uniform reference stress over the zone of tension ahead of the notch tip. Creep rupture and creep crack growth data alone are required and used to make the predictions. It is found that the shape of the crack growth curve is correctly predicted when mean data are employed. However, upper bound crack growth properties are required to accurately predict the actual extent of cracking. Sensitivity studies show that the amount of stress relief cracking predicted is relatively insensitive to the reference stress initially assumed to describe the residual stress distribution, since the reference stress relaxes to a magnitude that is almost independent of its initial value. Adoption of an initial reference stress equal to the ultimate tensile strength of the steel, when combined with mean creep rupture and upper bound crack growth properties, results in safe predictions that are not overly conservative. The analysis should only be regarded as reliable for small amounts of crack extension of less than the size of the tensile zone ahead of the crack tip.     

Retardation of a crack with connections between the faces using an induced thermoelastic stress field

This paper considers local temperature variations near the tip of a crack in the presence of regions in which the crack faces interact. It is assumed that these regions are adjacent to the crack tip and are comparable in size to the crack size. The problem of local temperature variations consists of delay or retardation of crack growth. For a crack with connections between the crack faces subjected to external tensile loads, an induced thermoelastic stress field, and the stresses at the connections preventing crack opening, the boundary-value problem of the equilibrium of the crack reduces to a system of nonlinear singular integrodifferential equations with a Cauchy kernel. The normal and tangential stresses at the connections are found by solving this system of equations. The stress intensity factors are calculated. The energy characteristics of cracks with tip regions are considered. The limiting equilibrium condition for cracks with tip regions is formulated using the criterion of limiting stretching of the connections.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 133–143, January–February, 2005     

J-integral and crack driving force in elastic–plastic materials

This paper discusses the crack driving force in elastic–plastic materials, with particular emphasis on incremental plasticity. Using the configurational forces approach we identify a “plasticity influence term” that describes crack tip shielding or anti-shielding due to plastic deformation in the body. Standard constitutive models for finite strain as well as small strain incremental plasticity are used to obtain explicit expressions for the plasticity influence term in a two-dimensional setting. The total dissipation in the body is related to the near-tip and far-field J-integrals and the plasticity influence term. In the special case of deformation plasticity the plasticity influence term vanishes identically whereas for rigid plasticity and elastic-ideal plasticity the crack driving force vanishes. For steady state crack growth in incremental elastic–plastic materials, the plasticity influence term is equal to the negative of the plastic work per unit crack extension and the total dissipation in the body due to crack propagation and plastic deformation is determined by the far-field J-integral. For non-steady state crack growth, the plasticity influence term can be evaluated by post-processing after a conventional finite element stress analysis. Theory and computations are applied to a stationary crack in a C(T)-specimen to examine the effects of contained, uncontained and general yielding. A novel method is proposed for evaluating J-integrals under incremental plasticity conditions through the configurational body force. The incremental plasticity near-tip and far-field J-integrals are compared to conventional deformational plasticity and experimental J-integrals.     

受载高聚物裂尖的损伤和银纹化

采用扫描电子显微镜(SEM)，对高聚物裂尖银纹损伤的引发和演化过程进行了原位观测．将固态高聚物本体材料视为线黏弹体，裂尖银纹区视为非线性损伤区，通过构造银纹区的损伤演化方程，给出了银纹区应力模型和银纹生长规律，数值结果与已有实验吻合良好。     

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.     

Nonlocal elasticity and dislocation image force due to cracks

Summary   Fundamental field equations of nonlocal elasticity are presented. With these equations, the image force on a screw dislocation due to a crack is analyzed using the conformal mapping technique. Two cases are considered: one is for a finite-length crack, the other is for an infinite one. All classical singularities of the dislocation image force are eliminated when the dislocation tends to the crack tip. The maximum of the force is obtained at the crack tip. Received 10 June 1999; accepted for publication 8 February 2000