Crack Tip Energy Release Rate Research Articles

Subcritical crack growth and arrest in the presence of a material interface

Reservoir systems often consist of layered rock formations that are naturally fractured. These can include both fractures that are confined within the main reservoir layer, and ones that penetrate adjacent confining layers or cut through into nearby reservoir strata. Layer-bound fractures have the effect of improving the overall permeability of a reservoir layer, however through-cutting fractures act as pathways for both fluid leakage and pressure communication between otherwise isolated formations. In this study, we investigate the subcritical propagation of a single crack from a stiff inner layer into more compliant and ductile outer layers. We model the crack growth numerically, by making use of recently formulated correction factors that account for the effect of mechanical boundaries on the crack tip energy release rate. Furthermore, we utilize a modified arc-length method to handle the stiff behaviour of the differential equations governing crack tip motion in a layered medium. Under different conditions, a fracture may be arrested permanently or temporarily at the layer boundary, propagate a short distance into the outer layer before arrest, or propagate critically in the outer layer forming a through-cutting fracture. We find that fractures are most likely to remain layer-bound in layers less than 5 m thick, a subcritical index below 10, and a low critical energy release rate relative to the confining layers. If the outer layer modulus is less than half that of the inner layer, the fracture is more likely to propagate a short distance into the confining layer before arrest. In the case of tectonic deformation characterized by steadily increasing far-field extensional strain, crack arrest at the layer boundary is likely to be only temporary, and the occurrence of layer-bound versus through-cutting fractures will be determined by the duration of said deformation together with the thickness and mechanical properties of the different layers.

Performance evaluation of a 20m-T Section bridge beam strengthened by HB-FRP

ABSTRACT The multi T-beam finite element model with an initial crack was generated based on the element and direct methods. The element method was used to evaluate the bonding performance of the fibre reinforced plastic (FRP)-to a concrete interface. On the other hand, the direct method introduced the basic theory of elastic fracture mechanics and calculated the crack tip energy release rate of the initial crack. In addition, the crack propagation risk before and after hybrid bonding FRP (HB-FRP) reinforcement was discussed. The simulation results showed that under traffic load, the bonding stress of FRP-concrete interface is very small in the absence of an initial crack, but the intermediate crack (IC) debonding is easier occurred at the flexural crack of the beam mid-span. With the function of the mechanical fastener, the interface debonding was suppressed with regard to overloading less than 4 times the design traffic load. Furthermore, it was shown that the higher the crack was, the greater the G I value was at the crack tip, which means a more unstable the crack was, and the easier it was to propagate. Also, the higher the initial crack was, the weaker the effect of HB-FRP reinforcement was in suppressing crack propagation.

Poroelastic effects on steady state crack growth in polymer gels under plane stress

Fracture experiments on polymer gels are often conducted with thin specimens, which are close to plane stress in two-dimensional models. However, many of the previous theoretical and numerical studies on fracture of polymer gels have assumed plane strain conditions. The subtle differences between the plane stress and plane strain conditions are elucidated in this paper based on a linear poroelastic formulation for polymer gels, including the asymptotic crack-tip fields and finite element simulations of steady-state crack growth in long strip specimens. Moreover, a poroelastic cohesive zone model is adopted to study the rate-dependent fracture process of polymer gels. It is found that, without the cohesive zone model, the normalized crack-tip energy release rate at the fast crack limit is greater than the slow crack limit, suggesting reduced poroelastic toughening for fast crack growth under plane stress conditions, while the two limits are identical under plane strain conditions. With a solvent-permeable cohesive zone for the case of immersed specimens, solvent diffusion within the cohesive zone enhances the poroelastic toughening significantly as the crack speed increases, leading to a rate-dependent traction-separation relation. On the other hand, with no solvent diffusion in the cohesive zone for the not-immersed case, the poroelastic toughening effect diminishes as the crack speed increases. Based on the present study, the intrinsic steady-state fracture toughness of a poroelastic gel can be determined using long-strip pure-shear specimens, which in general is smaller than the applied energy release rate.

Poroelastic Effects on the Time- and Rate-Dependent Fracture of Polymer Gels

AbstractFracture of polymer gels is often time- and rate-dependent. Subject to a constant load, a gel specimen may fracture immediately or after a delay (time-dependent, delayed fracture). When a crack grows in a gel, the fracture energy may depend on the crack speed (rate-dependent). The underlying mechanisms for the time- and rate-dependent fracture of gels could include local molecular processes, polymer viscoelasticity, and solvent diffusion coupled with deformation (poroelasticity). This paper focuses on the effects of poroelasticity. A path-independent, modified J-integral approach is adopted to define the crack-tip energy release rate as the energetic driving force for crack growth in gels, taking into account the energy dissipation by solvent diffusion. For a stationary crack, the energy release rate is time-dependent, with which delayed fracture can be predicted based on a Griffith-like fracture criterion. For steady-state crack growth in a long-strip specimen, the energy release rate is a function of the crack speed, with rate-dependent poroelastic toughening. With a poroelastic cohesive zone model, solvent diffusion within the cohesive zone leads to significantly enhanced poroelastic toughening as the crack speed increases, rendering a rate-dependent traction-separation relation. While most of the results are based on a linear poroelastic formulation, future studies may extend to nonlinear theories with large deformation. In addition to the poroelastic effects, other mechanisms such as viscoelasticity and local fracture processes should be studied to further understand the time and rate-dependent fracture of polymer gels.

Analytical model for estimation of energy release rate at mode I crack tip in bi-material of identical steels joined by an over-matched weld interlayer

Structure fabricated by welding identical steels or a fractured steel component repaired by steel weld filler of different strength leads to the presence of two interfaces with strength mismatch across them. Mode I crack in such a bi-material upon growing across the weld interlayer experiences the effect of the interfaces that manifests by way of change in crack tip energy release rate from the far field or remote value. The paper presents a strain based analytical model for estimation of the effect of interface over the crack tip. Crack tip energy release rate is determined at all the positions of the crack under SSY or K dominant conditions. The weld interlayer is assumed to be homogeneous and over-matched which possesses higher strength than that of the constituent steels. The modulus of elasticity is same throughout the domain. Edge crack of various discrete lengths is investigated in infinite body under uniform monotonic tension of 150 MPa in plane stress situation for demonstration of the model behavior.

Temperature and exposure-dependent interfacial fracture toughness model for thermal barrier coatings

An interfacial fracture toughness model for thermal barrier coatings (TBCs) is proposed in which model parameters not only include the effect of high temperature and exposure period of TBCs but also demonstrate the mode mixity characteristics. The model is expressed in terms of the Arrhenius-type form showing a temperature-dependent feature and also exhibits a dependence of microcrack density distributed along the coating interface. Two scaling parameters are used in formulating the model, one is introduced to link dislocation Burgers vector to the crack tip opening displacement (CTOD), the other is utilized to describe the crack tip energy release rate associated with the P-N force responsible for dislocation movement. These scaling parameters can be obtained by fitting to the interfacial fracture toughness data at ambient temperature and the CTOD, respectively. Since the experimentally measured microcrack density exhibits thermal cycle dependent behavior, an attempt is made to explain the experimentally obtained toughness values using the proposed interfacial crack toughness model. The model predicts an increase in fracture toughness with exposure temperature and mode mixity. The limitation of the model and possible improvement scheme are discussed.

A Fluid-Solid-Magnetic Coupling Algorithm of Internal Crack Growth in the Weld of Oil and Gas Pipelines

In order to characterize the dynamic process of the crack growth in the weld of oil and gas pipelines, a mathematical model of fluid-solid-magnetic multifield coupling was constructed in this paper. Based on this model, the bidirectional fluid-solid coupling and unidirectional magnetic structure coupling caused by the weld deformation were achieved by dynamic application of the fluid permeation pressure, calculating the internal crack growth in the pipe weld, reconstructing the computational grid near the internal crack, and discussing the characteristics of the magnetic leakage field in the process of the internal crack growth in pipe weld. Thus, a fluid-solid-magnetic coupling algorithm for the internal crack growth in pipe welds considering fluid permeation pressure is established. According to the characteristics of the internal crack opening distance, internal crack growth length, crack tip energy release rate, peak values of magnetic induction intensity level, and vertical component, the process of the internal crack growth is measured. The results show that the fluid osmotic pressure accelerates the process of the internal crack growth and this algorithm can solve the problem of the characterization and evaluation of crack growth in pipe welds under fluid-solid-magnetic coupling action.

Dynamic crack tip fields, T-stress and energy release rate in anisotropy

Higher order crack tip stresses, displacements, T-stress and energy release rate with a constant speed in anisotropic materials are studied. The dynamic stresses and displacements are derived from the displacement potentials and higher order complex functions. Using the dynamic stress and displacement components, the dynamic T-stress and energy release rate are derived. The effects of fiber direction and crack speed on the stresses, displacements, T-stress and energy release rate are examined. The maximum values of stresses σxx and σyy at crack tip around are greater when the direction of the stress component approaches to the fiber direction than when the direction of the stress component is dissimilar to the fiber direction. T-stress in anisotropic materials, unlike isotropic and orthotropic materials, appears in the stress term of mode II as well as mode I. Energy release rate GI for opening mode decreases as α increases and GII for shearing mode increases as α increases.

A Linear Poroelastic Analysis of Time-Dependent Crack-Tip Fields in Polymer Gels

Based on a linear poroelastic formulation, we present an asymptotic analysis of the transient crack-tip fields for stationary cracks in polymer gels under plane-strain conditions. A center crack model is studied in detail, comparing numerical results by a finite element method to the asymptotic analysis. The time evolution of the crack-tip parameters is determined as a result of solvent diffusion coupled with elastic deformation of the gel. The short-time and long-time limits are obtained for the stress intensity factor and the crack-tip energy release rate under different chemo-mechanical boundary conditions (immersed versus not-immersed, displacement versus load controlled). It is found that, under displacement-controlled loading, the crack-tip energy release rate increases monotonically over time for the not-immersed case, but for the immersed case, it increases first and then decreases, with a long-time limit lower than the short-time limit. Under load control, the energy release rate increases over time for both immersed and not-immersed cases, with different short-time limits but the same long-time limit. These results suggest that onset of crack growth may be delayed until the crack-tip energy release rate reaches a critical value if the applied displacement or traction is subcritical but greater than a threshold.

Steady-state crack growth in polymer gels: A linear poroelastic analysis

Based on a linear poroelastic formulation, we present an asymptotic analysis of the crack tip fields for steady-state crack growth in polymer gels. A finite element method is then developed for numerical analysis. A semi-infinite crack in a long strip specimen subject to plane-strain loading is studied in detail. The crack-tip fields from the numerical analysis agree with the asymptotic analysis with a poroelastic stress intensity factor, which is generally smaller than the stress intensity factor predicted by linear elasticity due to poroelastic shielding. Similarly, the crack-tip energy release rate calculated by a modified J-integral method is smaller than the applied energy release rate. The size of the poroelastic crack-tip field (or K-field) is characterized by a diffusion length scale that is inversely proportional to the crack speed. For relatively fast crack growth, the diffusion length is small compared to the strip thickness (small-scale diffusion), and the poroelastic K-field transitions to an elastic K-field at a distance proportional to the diffusion length. In this case, the crack-tip energy release rate decreases with increasing crack speed under the same loading condition. For relatively slow crack growth, the diffusion length is greater than the strip thickness (large-scale diffusion), and the poroelastic crack-tip field is confined and transitions to a one-dimensional diffusion zone ahead of the crack tip. In this case, the energy release rate increases with increasing crack speed. Both immersed and not-immersed crack face conditions are considered. Under the same loading conditions, the poroelastic stress intensity factor and the modified J-integral are higher for the immersed case than not-immersed, but they approach the same values at the fast and slow crack limits. In general, if the crack-tip energy release rate is taken to be the intrinsic fracture toughness of the gel, the applied energy release rate as the apparent fracture toughness is greater due to energy dissipation associated with solvent diffusion, which is referred to as poroelastic toughening. It is proposed that the modified J-integral can be used to determine the intrinsic fracture toughness of the gel in experiments, which may or may not depend on crack speed. Moreover, the present results are found to be qualitatively consistent with previous experiments on the effects of solvent viscosity and crack-tip soaking.

Finite element investigation on mode I crack tip characteristics in residually stressed glare

PurposeBehavior of mode I crack tip in fiber metal laminate (FML) differs from that in homogeneous or plain specimen made of metal used in the laminate due to the load transfer effect in the laminate caused by property mismatch between dissimilar material layers. The purpose of this paper is to present a finite element investigation on the characteristics of crack tip in monotonically loaded and residually stressed FML.Design/methodology/approachCrack tip characteristics are assessed by: the sizes of various zones that form at the tip; and crack tip energy release rates. The same are found by modeling two types of Glare laminates under monotonic tension with different crack orientations in SSY regime – Type I and Type II. Residual stresses are externally introduced in the models. Delaminations are modeled by cohesive elements. Crack tip zone sizes are measured from finite element solutions. Values of J integrals are computed over cyclic paths near the crack tips. Identically cracked and loaded plain aluminum alloy specimens are also modeled for comparison.FindingsThe sizes of crack tip zones in Glare laminates are found to be different than those in plain specimens. Process zone is observed to form at crack tip in Type I laminate whereas it does not develop in Type II laminate, the reverse being true in plain specimens. Values of J integrals near crack tips are also found to deviate from those in plain specimens, higher in Type I laminate due to crack tip stress amplification and lower in Type II laminate due to stress reduction. Crack orientation decides the amplification or shielding effect in the laminate.Research limitations/implicationsThere is scope for validating the numerical results reported in the paper by theoretical models.Practical implicationsThe method to quantify crack tip shielding and amplification is presented that shall be useful in checking the structural integrity/safety of the laminate during actual service conditions.Originality/valueShielding and amplification effects are explicitly described and illustrated in the paper. Suitability of using J integrals over paths crossing non-homogeneous and property mismatched material layers is tested. Use of cohesive zone method that is readily applicable in finite element procedures and is relatively simple, fast and reasonably accurate is also demonstrated.

On the fracture toughness and stable crack growth in shape memory alloy actuators in the presence of transformation-induced plasticity

The effect of transformation-induced plasticity (TRIP) on the fracture response of polycrystalline shape memory alloys is analyzed in the prototype infinite center-cracked plate subjected to thermal cycling under constant mechanical loading in plain strain. Finite element calculations are carried out to determine the mechanical fields and the crack-tip energy release rate using the virtual crack closure technique. Similar to phase transformation, TRIP is found to affect both the driving force for crack growth and the crack growth kinetics by promoting crack advance when occurring in a fan in front of the crack tip and providing a “shielding” effect when occurring behind that fan. Accumulation of TRIP strains over the cycles results in higher energy release rates from one cycle to another and may result in crack growth if the crack-tip energy release rate reaches a material “specific” critical value after a sufficient number of cycles. During crack advance, the shielding effect of the TRIP strains left in the wake of the growing crack dominates and therefore TRIP is found to both promote the initiation of crack growth and extend the stable crack growth regime.

An Accurate Thermomechanical Model for Laser-Driven Microtransfer Printing

A recently developed transfer printing technique, laser-driven noncontact microtransfer printing, which involves laser-induced heating to initiate the separation at the interface between the elastomeric stamp (e.g., polydimethylsiloxane (PDMS)) and hard micro/nanomaterials (e.g., Si chip), is valuable to develop advanced engineering systems such as stretchable and curvilinear electronics. The previous thermomechanical model has identified the delamination mechanism successfully. However, that model is not valid for small-size Si chip because the size effect is ignored for simplification in the derivation of the crack tip energy release rate. This paper establishes an accurate interfacial fracture mechanics model accounting for the size effect of the Si chip. The analytical predictions agree well with finite element analysis. This accurate model may serve as the theoretical basis for system optimization, especially for determining the optimal condition in the laser-driven noncontact microtransfer printing.

Damage-tolerant composite design principles for aircraft components under fatigue service loading using multi-scale progressive failure analysis

Virtual testing has lately gained widespread acceptance among scientists as a simple, accurate, and reproducible method to determine the mechanical properties of heterogeneous microstructures, early in the production process. As a result of the rapid expansion of the use of composites in aerospace design, virtual testing techniques are, in fact, deemed extremely useful to eliminate unnecessary tests and to reduce cost and time associated with generating allowables for lengthy lifing analyses of structures. Leveraging on a limited set of experimental data, a Progressive Failure Analysis can accurately predict the life and safety of a component/assembly, simply tapping on the physics of its micro-/macro- mechanics material properties, manufacturing processes, and service environments. The robust methodology is showcased using blind predictions of fatigue stiffness degradation and residual strength in tension and compression after fatigue compared with test data from Lockheed Martin Aeronautics and Air Force Research Laboratory). The multi-scale progressive failure analysis methodology in the GENOA software considers uncertainties and defects and evaluated the damage and fracture evolution of three IM7-977-3 laminated composite layups at room temperature. The onset and growth of composite damage was predicted and compared with X-ray CT. After blind predictions, recalibrations were performed with knowledge of the test data using the same set of inputs for all layups and simulations. Damage and fracture mechanism evolution/tracking throughout the cyclic loading is achieved by an integrated multi-scale progressive failure analysis extended FEM solution: (a) damage tracking predicts percentage contributing translaminar and interlaminar failure type, initiation, propagation, crack growth path, and observed shift in failure modes, and (b) fracture mechanics (VCCT, DCZM) predicts crack growth (Crack Tip Energy Release Rate vs. Crack Length), and delamination. The predictive methodology is verified using a building block validation strategy that uses: (a) composite material characterization and qualification (MCQ) software, and (b) the GENOA multi-scale progressive failure analysis fatigue life, stiffness degradation, and post-fatigue strength predictions for open-hole specimens under tension/compression at RTD. The unidirectional tension, compression, and in-plane shear lamina properties supplied by Lockheed Martin Aeronautics and the Air Force Research Laboratory (based on the D3039, D638, D3518 tests) were used by MCQ to reverse engineer effective fiber and matrix static and fatigue properties for the IM7-977-3 material system. The use of constituent properties identified the root cause problem for composite failure and enabled the detection of damage at the micro-scale of the material where damage is incepted. For all three case studies (namely, layups [0/45/90/−45]2s, [+60, 0, −60]3s, and [+30, +60, 90, −60, −30]2s), the blind predictions on the fatigue stiffness degradation and residual strength of the open-hole coupon in tension/compression under cyclic loading (with R = 0.1) at RTD were evaluated using a FE mesh (made of 2k shell elements), in which only one shell element, containing all plies, was employed through the thickness. The results of all analyses correlated very well with the tests, including the damage micro-graphs generated during the cyclic loading.

Stable Crack Growth During Thermal Actuation of Shape Memory Alloys

A finite element analysis of crack growth is carried out in shape memory alloys subjected to thermal variations under plane strain, mode I, constant applied loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate which is modeled using the virtual crack closure technique. The load level, applied at a high temperature at which the austenite phase is stable, is assumed sufficiently low so that the resulting crack-tip energy release rate is smaller than the critical value but sufficiently high so that the critical value is reached during cooling, initiating crack growth (Baxevanis and Lagoudas in Int J Fract 191:191–213, 2015). Stable crack growth is observed, mainly associated with the shielding effect of the transformed material left in the wake of the advancing crack. Results pertaining to the near-tip mechanical fields and fracture toughness are presented and their sensitivity to phase transformation metrics and bias load levels is investigated.

On the driving force for crack growth during thermal actuation of shape memory alloys

The effect of thermomechanically induced phase transformation on the driving force for crack growth in polycrystalline shape memory alloys is analyzed in an infinite center-cracked plate subjected to a thermal actuation cycle under mechanical load in plain strain. Finite element calculations are carried out to determine the mechanical fields near the static crack and the crack-tip energy release rate using the virtual crack closure technique. A substantial increase of the energy release rate – an order of magnitude for some material systems – is observed during the thermal cycle due to the stress redistribution induced by large scale phase transformation. Thus, phase transformation occurring due to thermal variations under mechanical load may result in crack growth if the crack-tip energy release rate reaches a material specific critical value.

Numerical study of thermo-mechanical coupling effects on crack tip fields of mixed-mode fracture in pseudoelastic shape memory alloys

The thermo-mechanical coupling effects on mixed-mode crack tip parameters in pseudoelastic shape memory alloys are studied by a finite element solution. Different loading rates are applied on the K-dominant part of the small scale transformation region. Both plane strain and plane stress analyses are carried out to study how the coupling between thermal and mechanical regimes alters the near tip fields in the martensitic region. The crack tip energy release rate and the J-integral remain history-dependent. The stress/strain response, the angular distributions of the stress and the released temperature, the shape of the transformation zone and the released temperature are selected as the crack tip fields of interest. Special attention is given to study of how the aforementioned crack tip fields are affected by the increase of applied loading rate. A comparison is also drawn between the crack tip fields in plane strain and plane stress states to complete the discussion.

Numerical analysis of crack tip fields in interface fracture of SMA/elastic bi-materials

The problem of an interface crack between a shape memory alloy and an elastic layer is numerically addressed. The shape memory alloy behavior is modeled with a continuum thermodynamics based constitutive model embedded within the finite element method. With the help of the boundary layer approach, and the assumption of small scale transformation zone, the K-dominated region in the tip of the interface crack is loaded under general mixed-mode condition. Both slow and fast loading rates are considered to study the effects of thermo-mechanical coupling on the interface crack tip fields, especially the crack tip energy release rate within a history-dependent J-integral framework, the stress/strain curve during the loading process, and the shape and size of the transformation zone and the heated zone. A special effort is made to investigate how changing the rate of applied loading, the mode-mixity, and the material properties of SMA and elastic layer modify the crack tip fields.

On the Effect of Latent Heat on the Fracture Toughness of Pseudoelastic Shape Memory Alloys

A finite element analysis of steady-state crack growth in pseudoelastic shape memory alloys under the assumption of adiabatic conditions is carried out for plane strain, mode I loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate and the fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip critical value. Results related to the influence of latent heat on the near-tip stress field and fracture toughness are presented for a range of parameters related to thermomechanical coupling. The levels of fracture toughness enhancement, associated with the energy dissipated by the transformed material in the wake of the growing crack, are found to be lower under adiabatic conditions than under isothermal conditions [Baxevanis et al., 2014, J. Appl. Mech., 81, 041005]. Given that in real applications of shape memory alloy (SMA) components the processes are usually not adiabatic, which is the case with the lowest energy dissipation during a cyclic loading–unloading process (hysteresis), it is expected that the actual level of transformation toughening would be higher than the one corresponding to the adiabatic case.

Crack solutions and weight functions for plane problems in three-dimensional quasicrystals

The plane problems of an elliptic hole and a crack in three-dimensional quasicrystals subject to far-field loadings are studied. The generalized Stroh formalism is adopted here, and the explicit solutions for the coupled fields are obtained in the closed form. When the elliptic hole reduces to a crack, the analytical expressions for both the entire fields and the asymptotic fields near the crack tip are determined. The crack theory of quasicrystals, including the determination of the field intensity factors, crack opening displacements, crack tip energy release rates and so on, is a prerequisite. Applying Betti’s theorem of reciprocity, the weight functions for a quasicrystal body with a crack are derived. The weight functions provide a means of calculating the intensity factors for the crack when both phonon and phason point forces are imposed at arbitrary locations.