A cohesive plastic and damage zone model for dynamic crack growth in rate-dependent materials

Mode I steady-state dynamic crack growth in rate-dependent viscoplastic solids containing damage, under small scale yielding conditions, is analyzed based on a modified cohesive zone model. A multi-scale approach is used to describe the entire non-linear zone consisting of a plastic region and a damage region, each of which has its own constitutive law. Traction in the damage region is characterized by a softening power-law, in terms of the ultimate strength, a softening index and a rate sensitivity factor. In the plastic region, the cohesive law is assumed to be both strain hardening and rate dependent. The critical crack opening displacement at the physical crack-tip controls crack growth. The governing integral equations are derived and solved by a collocation method combined with associated boundary conditions. Numerical results are presented for the traction and opening profiles along the cohesive zone, the fracture energy and lengths of the damage and non-linear zones at different crack speeds and for different material parameters. The importance of factors, such as material softening, plastic deformation, crack speed and viscosity, is identified by parametric studies. In addition, the competition of plastic flow and material damage, and its effect on crack growth, are discussed.     

A refined cohesive zone model that accounts for inertia of cohesive zone of a moving crack

Existing cohesive zone models assume that actual fracture zone of non-zero mass can be modeled by a line segment (cohesive zone) with no mass and inertia. In the present work, a simplified mass-spring model is presented to study inertia effect of cohesive zone on a mode-I steady-state moving crack. It is showed that fracture energy predicted by the present model increases dramatically when a finite limiting crack speed is approached. Reasonable agreement with known experiments indicates that the present model has the potential to catch the inertia effect of cohesive zone which has been ignored in existing cohesive zone models and better simulate dynamic fracture at high crack speed.     

Plasticity induced fatigue crack growth retardation model for steel elements reinforced by composite patch

Fatigue tests on notched steel plates reinforced by composite patch showed that the application of carbon fiber reinforced polymers (CFRP) strips with pretension of the overlays prior to bonding. This resulted in a significant amount of additional fatigue life. In particular, the pre-tension produces a compressive field in the steel plate which reduces the stress ratio that enhances crack growth retardation. The fatigue crack propagation rate is postulated to be a function of the effective strain energy density factor range. Fatigue crack growth data showed that standard crack growth retardation model cannot be used to evaluate the minimum effective stress. Hence, an ad hoc plasticity model is introduced and validated using experimental results. The proposed technique is an extension of the well know Newman’s model. The bridging effect due to the reinforcing strips is analytically modeled in order to estimate the reduction of crack opening displacement and finally the magnification of the crack growth retardation. Numerical and experimental results match well and show a significant influence of the pre-tension level on the expected fatigue crack growth rate of a reinforced steel plate.     

Inverse parameter identification of cohesive zone model for simulating mixed-mode crack propagation

Inverse analysis is widely applied to the identification of material properties or model parameters. In order to improve the computational efficiency of the inverse method based on the genetic algorithm, an interpolation scheme upon the response surface constructed by the finite element simulation has been adopted in this paper. Meanwhile, a gradual homogenization treatment scheme has also been presented to improve the convergence of the inverse method based on the Kalman filter algorithm. Both methods are proven effective in dealing with the single-objective inverse problem. However, literature studies show that the adoption of multiple types of experimental information is useful to improve the accuracy of inverse analysis. In this case, it turns into a multiple-objective inverse problem. Our practice proved that the above-mentioned two methods might not yield a proper result if the sensitivity issue of different types of information is not considered. Therefore, another multi-objective inverse method, in combination of the above two optimization algorithms and a weight-estimating scheme that can consider such sensitivity, has been further presented. Finally, by using a mixed-mode crack propagation simulation and two types of experimental information (loading-displacement response curve and crack path profile), the parameters of the cohesive zone model were inversely identified and its simulation results are in good agreement with the experiment.     

A penny-shaped cohesive crack model for material damage

A novel micromechanics based damage model is proposed to address failure mechanism of defected solids with randomly distributed penny-shaped cohesive micro-cracks (Barenblatt–Dugdale type). Energy release contribution to the material damage process is estimated in a representative volume element (RVE) under macro hydrostatic stress state. Macro-constitutive relations of RVE are derived via self-consistent homogenization scheme, and they are characterized by effective nonlinear elastic properties and a class of pressure sensitive plasticity which depends on crack opening volume fraction and Poisson’s ratio. Several distinguished features of the present model are compared with Gurson model and Gurson–Tvergaard–Needleman (GTN) model, showing that the proposed model can better capture material degradation and catastrophic failure due to cohesive micro-crack growth and coalescence.     

One model of fatigue crack growth

A model for crack growth is proposed based on studies of the variation in the curvature radius at the crack tip during cyclic loading. Relations are obtained between mechanical material characteristics, crack geometry, and the rate of crack growth in a structure under cyclic loading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 167–175, July–August, 2009.     

A stochastic Markovian model for fatigue short crack growth across microstructural barriers

A stochastic model for fatigue short crack growth is presented. It takes into account the interaction between the crack-tip plastic zone and grain boundaries. The process is Markovian. It is completely described by the crack length and the size of the plastic zone. The integro-differential equation giving the evolution of the transition probability distribution is derived.     

A thermomechanical cohesive zone model for bridged delamination cracks

The coupled thermomechanical numerical analysis of composite laminates with bridged delamination cracks loaded by a temperature gradient is described. The numerical approach presented is based on the framework of a cohesive zone model. A traction-separation law is presented which accounts for breakdown of the micromechanisms responsible for load transfer across bridged delamination cracks. The load transfer behavior is coupled to heat conduction across the bridged delamination crack. The coupled crack-bridging model is implemented into a finite element framework as a thermomechanical cohesive zone model (CZM). The fundamental response of the thermomechanical CZM is described. Subsequently, bridged delamination cracks of fixed lengths are studied. Values of the crack tip energy release rate and of the crack heat flux are computed to characterize the loading of the structure. Specimen geometries are considered that lead to crack opening through bending deformation and buckling delamination. The influence of critical mechanical and thermal parameters of the bridging zone on the thermomechanical delamination behavior is discussed. Bridging fibers not only contribute to crack conductance, but by keeping the crack opening small they allow heat flux across the delamination crack to be sustained longer, and thereby contribute to reduced levels of thermal stresses. The micro-mechanism based cohesive zone model allows the assessment of the effectiveness of the individual mechanisms contributing to the thermomechanical crack bridging embedded into the structural analysis.     

Steady growth of a crack with a rate and temperature sensitive cohesive zone

The steady-state dynamic propagation of a crack in a heat conducting elastic body is numerically simulated. Specifically, a mode III semi-infinite crack with a nonlinear temperature dependent cohesive zone is assumed to be moving in an unbounded homogeneous linear thermoelastic continuum. The numerical results are obtained via a semi-analytical technique based on complex variables and integral transforms. The relation between the thermo-mechanical properties of the failure zone and the resulting crack growth regime are investigated. The results show that temperature dependent solutions are substantially different from purely mechanical ones in that their existence and stability strongly depends on the cohesive zone thermal properties.     

An improved atomistic simulation based mixed-mode cohesive zone law considering non-planar crack growth

A novel and improved atomistic simulation based cohesive zone law characterizing interfacial debonding is developed which explicitly accounts for the non-planarity of the crack propagation. Group of atoms in the simulation constituting cohesive zones which are used to obtain local stress and crack opening displacement data are determined dynamically during the non-planar crack growth as they cannot be determined apriori. The methodology is used to study the debonding of Σ5 (2 1 0)/[0 0 1] symmetric tilt grain boundary interface in a Cu bicrystal under several mixed mode loading conditions. Simulations show that such bicrystalline specimen exhibits three types of energy dissipative mechanisms – shear coupled GB migration (SCM) away from the crack-tips, change in spacial orientation of GB structural units rendering highly disordered grain boundary near the crack tips and brittle intergranular fracture. Which combination of these three deformation mechanism will be active influencing the degree of non-planarity of the crack propagation at various stages of loading depends on the loading mode-mixity. As the ratio of shear component of the loading parallel to the GB plane and normal to the tilt axis with respect to the normal loading increases (thereby increasing the mode-mixity), overall strain-to-failure also increases and SCM tends to become the dominant deformation mechanism. Through this framework, analytical functional forms and parameters describing cohesive laws for both normal and shear traction as a function of the mode-mixity of the loading and crack opening displacement are predicted.     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

Stratified model for estimating fatigue crack growth rate of metallic materials

Introduction Thefatiguedestructionisoneofthemaintypesofthemetaldamage.Therelationcurve betweenthefatiguecrackgrowthrateda/dNandthestressstrengthfactoramplitudeΔKisthe importantdatiumoffatiguecapabilityindesigningthemetaldamagetolerantlimitsandpredicting thelifeofmetalcomponentparts.Duetovariabilityofthefatiguecrackgrowthrate,alarge amountoftestsamplesareusuallyrequiredtoderiveahighlyreliableda/dN_ΔKcurve. However,inmostactualengineeringpractice,itishardtofindmultiplespecimenswithvery simil…     

A generalized Paris’ law for fatigue crack growth

An extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wöhler SN curve of the material, suggesting a more general “unified law”. In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Δa, the “fracture quantum”. In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Δa, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture “quantum” on the applied stress range level such that the correct convergence towards the Wöhler-like regime is obtained. Hence, the final law includes both Wöhler's and Paris’ material constants, and can be seen as either a generalized Wöhler's SN curve law in the presence of a crack or a generalized Paris’ law for cracks of any size.     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.     

Thermodynamic-based cohesive zone healing model for self-healing materials

This work presents a thermodynamic-based cohesive zone framework to model healing in materials that tend to self-heal. The nominal, healing and effective configurations of continuum damage-healing mechanics are extended to represent cohesive zone configurations. To incorporate healing in a cohesive zone model, the principle of virtual power is used to derive the local static/dynamic macroforce balance and the boundary traction as well as the damage and healing microforce balances. A thermodynamic framework for constitutive modeling of damage and healing mechanisms of cracks is used to derive the evolution equations for the damage and healing internal state variables. The effects of temperature, resting time, crack closure, history of healing and damage, and level of damage on the healing behavior of the cohesive zone are incorporated. The proposed model promises solid basis for understanding the self-healing phenomena in self-healing materials.     

A new photoelastic model for studying fatigue crack closure

The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.     

A methodology for thermomechanical fatigue crack growth testing in MMCs

This paper describes the experimental techniques used in an investigation of the crack growth characteristics of a four-ply, unidirectional, silicon carbide fiber reinforced, titanium matrix composite (SCS-6/Ti–6Al–2Sn–4Zr–2Mo) subjected to thermomechanical fatigue. A mechanical test system was assembled which is capable of conducting fully automated, computer-controlled thermomechanical fatigue crack growth tests. The system is able to simultaneously impose operator-defined arbitrary mechanical and thermal histories on the specimen. Crack lengths in single-edge tension [SE(T)] or middle tension [M(T)] specimens are measured by the direct-current electric potential method and optically using a unique telemicroscope system. A series of isothermal, in-phase and out-of-phase crack growth tests was conducted to obtain baseline data for material modeling purposes. The test temperatures ranged from 150°C to 538°C, and the highest thermal frequency was 0.0083 Hz.     

A technique to measure fatigue crack growth threshold

An experimental technique for determining fatigue crack growth threshold is presented. This experimental technique uses an increasing ΔK step loading procedure to determine threshold going from a no-growth to growth status. Stress relief annealing of the Ti-6AI-4V test specimens eliminates load history effects normally associated with the precrack, providing a measurement equivalent to what is achieved by a standard ASTM load shed test. In addition to measuring load history free thresholds, this increasing ΔK technique can be used to investigate different load history effects on threshold by using the threshold step measurement with different precrack histories and without the subsequent annealing process. Verification of the threshold step measurement is demonstrated by comparing measurements with standard ATSM load shed testing results.