Damage Zone Model Research Articles

Electrically anisotropic structure of the Rocky Mountain Trench near Valemount, British Columbia inferred from magnetotellurics: implications for geothermal exploration

Canoe Reach is a region of high geothermal potential on a segment of the Southern Rocky Mountain Trench fault (SRMTF) with highly metamorphosed and structurally complex wall rocks, near Valemount, British Columbia. This study contains analyses of magnetotelluric data collected at Canoe Reach accounting for electrical anisotropy, which is not often considered during geothermal exploration. Isotropic and anisotropic 3D inversions are used due to signs of electrical anisotropy in the Canoe Reach magnetotelluric data and the presence of visibly anisotropic geological structure. At Canoe Reach North, the anisotropic model is preferred for its simpler structure and consistency with the mapped geology. An anisotropic feature in the footwall of the steeply southwest-dipping SRMTF has a low resistivity in the fault-perpendicular direction and a high resistivity in the vertical direction, which is more easily explained by conductive minerals than by fluids in the highly metamorphosed gneiss. An exploration well in the SRMTF footwall encountered two graphite seams with thicknesses ≥1 m, supporting the interpretation of anisotropic resistivity due to conductive minerals. A strong resistivity contrast across the SRMTF suggests juxtaposition of different lithologies, challenging existing interpretations of SRMTF displacement at Canoe Reach. At Canoe Reach South, anisotropic features near the Canoe River thermal spring with a high resistivity in the fault-perpendicular direction and low resistivity in the vertical direction are consistent with fault core and damage zone models. Magnetotelluric data may be sensitive to permeability anisotropy of fault zones, and the use of electrically anisotropic inversions should be considered for these settings.

Modified hyper-viscoelastic damage evolution constitutive model for polyurethane materials – an experimental and numerical investigation

Elastomeric materials are widely used in different industries due to their excellent capability to withstand different loading types. There are significant challenges to the efficient design of elastomeric structures because of the rate-dependent and highly nonlinear behavior of this type of material. In this study, a damage zone model was employed to simulate the material behavior and damage evolution in polyurethane (PU) elastomers with different shore hardness. This model consists of three sections, hyper viscoelastic constitutive model, damage initiation, and damage evolution using a hyper viscoelastic traction-separation law. To simulate the nonlinear behavior of PU, a dynamic increase factor (DIF) implemented into the Mooney–Rivlin strain density function with 9 parameters. The material characteristics are specified by performing the experimental tests for three different shore hardness. In this study, a user-defined subroutine (VUMAT) was developed to predict the damage evolution in the pure shear tearing specimen of PU elastomers. The results verification proves a good agreement between the FEA simulation and experimental data. Therefore, the developed numerical analysis procedure can be used to investigate the damage initiation and evolution in elastomeric materials.

Development and validation of a simulation methodology for composite joints with delamination arresting features

This paper presents the development of a modelling methodology in a finite element framework for the simulation of novel composite joints with delamination arresting features. The investigated composite joints employ the co-consolidation technique for the assembly of composite skins and stiffeners in a structural joint; in order to arrest and retard delamination damage evolution that may appear during service life, crack stopping features are included in the joint. Progressive damage modelling and cohesive zone modelling methodologies are employed for the analysis of intralaminar and interlaminar failure of laminate composite materials components. The modelling and simulation of experimental test cases available in the open literature are used for validation of the developed progressive damage and cohesive zone models through comparison of numerical results to respective experimental results for all test cases. The mechanical response of the butt-joint structural element is experimentally investigated and linear/nonlinear finite element models are developed to simulate its mechanical behaviour. The comparison between the experimental and numerical results demonstrates the applicability of the developed methodology in the simulation of novel composite structural joints with crack-stopping features.

Experimental and numerical investigations of micro-meso damage evolution for a WC/Co-type tool material

Commercial Co/WC/diamond composites with 90vol.% Co also belong to hard metals and, as a kind of tool materials, are very useful. Their deformation behavior can be both ductile and quasi-brittle, determined by the diamond portion and local morphology. Another characteristic is that submicron-sized WC particles, possessing non-negligible strengthening influence due to the size effect, cannot be fully present in a representative microstructure. This work emphasizes the local damage evolutions’ dependence on microstructural features. Rice&Tracey damage and cohesive zone model describe the ductile and quasi-brittle damage behavior. The mechanism-based strain gradient plasticity takes the size effect of submicron-sized WC particles into consideration. Both real and artificial microstructures are used. Besides homogeneous boundary conditions (BCs), the periodic BCs are also applied in a 2D damage simulation. This work proves that FE models with two phases, the homogenized Co-WC matrix and diamond particles, can correctly predict damage evolution. FE results show that the WC phase has a higher mean stress value than the diamond phase, which is proved by the nano-indentation test. From FE simulation results, local hot spots appear in the matrix closed to sharp diamond corners/edges and crossing regions of shear bands. The experimental and numerical results are compared on micro and macro scales. For the local strain distribution and the damage development, numerical predictions match the reality well, even in morphological details. Furthermore, since the published data about WC-Co type tool materials with Co>50vol.% are rare, the obtained knowledge in this work also contributes to the data collection.

Influence of Fault Zone Maturity on Fully Dynamic Earthquake Cycles

AbstractWe study the mechanical response of two‐dimensional vertical strike‐slip fault to coseismic damage evolution and interseismic healing of fault damage zones by simulating fully dynamic earthquake cycles. Our models show that fault zone structure evolution during the seismic cycle can have pronounced effects on mechanical behavior of locked and creeping fault segments. Immature fault damage zone models exhibit small and moderate subsurface earthquakes with irregular recurrence intervals and abundance of slow‐slip events during the interseismic period. In contrast, mature fault damage zone models host pulse‐like earthquake ruptures that can propagate to the surface and extend throughout the seismogenic zone, resulting in large stress drop, characteristic rupture extents, and regular recurrence intervals. Our results suggest that interseismic healing and coseismic damage accumulation in fault zones can explain the observed differences of earthquake behaviors between mature and immature fault zones and indicate a link between regional seismic hazard and fault structural maturity.

A theoretical and computational investigation of mixed mode creep crack growth along an interface

In this paper, we propose a theoretical framework for studying mixed mode (I and II) creep crack growth under steady state creep conditions. In particular, we focus on the problem of creep crack growth along an interface, whose fracture properties are weaker than the bulk material, located either side of the interface. The theoretical framework of creep crack growth under mode I, previously proposed by the authors, is extended. The bulk behaviour is described by a power-law creep, and damage zone models that account for mode mixity are proposed to model the fracture process ahead of a crack tip. The damage model is described by a traction-separation rate law that is defined in terms of effective traction and separation rate which couple the different fracture modes. Different models are introduced, namely, a simple critical displacement model, empirical Kachanov type damage models and a micromechanical based model. Using the path independence of the C^{*}-integral and dimensional analysis, analytical models are developed for mixed mode steady-state crack growth in a double cantilever beam specimen (DCB) subjected to combined bending moments and tangential forces. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models and a scaling function (C_{k}) is determined in terms of a dimensionless quantity phi _{0} (which is the ratio of geometric and material length scales), mode mixity chi and the deformation and damage coupling parameters. We demonstrate that the form of the C_{k}-function does not change with mode mixity; however, its value depends on the mode mixity, the deformation and damage coupling parameters and the detailed form of the damage zone. Finally, we demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments for mode I and II loading conditions.

Experimental and Numerical Investigations of Micro-Meso Damage Evolution for a WC/Co-Type Tool Material

Commercial Co/WC/diamond composites with 90vol.% Co also belong to hard metals and, as a kind of tool materials, are very useful. Their deformation behavior can be both ductile and quasi-brittle, determined by the diamond portion and local morphology. Another characteristic is that submicron-sized WC particles, possessing non-negligible strengthening influence due to the size effect, cannot be fully present in a representative microstructure. This work emphasizes the local damage evolutions’ dependence on microstructural features. Rice&Tracey damage and cohesive zone model describe the ductile and quasi-brittle damage behavior. The mechanism-based strain gradient plasticity takes the size effect of submicron-sized WC particles into consideration. Both real and artificial microstructures are used. Besides homogeneous boundary conditions (BCs), the periodic BCs are also applied in a 2D damage simulation. This work proves that FE models with two phases, the homogenized Co-WC matrix and diamond particles, can correctly predict damage evolution. FE results show that theWC phase has a higher mean stress value than the diamond phase, which is proved by the nano-indentation test. From FE simulation results, local hot spots appear in the matrix closed to sharp diamond corners/edges and crossing regions of shear bands. The experimental and numerical results are compared on micro and macro scales. For the local strain distribution and the damage development, numerical predictions match the reality well, even in morphological details. Furthermore, since the published data about WC-Co type tool materials with Co>50vol.% are rare, the obtained knowledge in this work also contributes to the data collection.

Experimental and numerical investigations of the mechanical behavior of half sandwich laminate in the context of blanking

In this study, the complex mechanical behavior of an aluminum/low-density polyethylene (LDPE) half sandwich structure was investigated during the blanking process. Mechanical tests were conducted for the polymer and metal layer and the delamination behavior of the adhesive between the two layers. A new testing device was designed for detecting the delamination under tensile mode. Corresponding finite element models were established for the mechanical tests of the metal layer and the delamination of both layers for inverse parameter identification. Material parameters for Lemaitre-type damage, Drucker-Prager, and cohesive zone models were identified for the metal, polymer, and adhesive, respectively. A finite-element (FE) model was established for the blanking process of the sandwich structures. The experimental force-displacement curves, obtained in the blanking process of the half sandwich sheet, were compared with the predicted results of the FE model. The results showed that the predicted force-displacement curves and the experimental results were in good agreement. Additionally, the correlation between cutting clearance and changes in the force-displacement curves was obtained. Three feature values quantitatively described the imperfection of the experimental cutting edge. The effect of punch clearance on these values was studied numerically and experimentally. The results indicated that a smaller clearance generated a better cutting-edge quality. The stress state of the half sandwich structure during blanking was analyzed using the established FE model.

Effect of weld angle on the creep rupture life of ferritic/austenitic dissimilar weld interfaces under remote mode I fracture

Dissimilar metal welded structures (DMWs) used extensively in conventional and nuclear power plants can suffer from in-service failures at the dissimilar interface with a much reduced life compared to similar metal weld counterparts at the same operating stress and temperature. This paper evaluates the effect of weld angle on the interface creep failure mode of two-dimensional DMW plates consisting of a ferritic steel P91 and an Inconel 82 filler metal within a finite element (FE) framework. A physical cavity growth damage zone model is developed to describe the damage accumulation at the interface, which naturally takes into account the local mode mixity. The material parameters are calibrated against standard 90° weld creep rupture data and used to predict the rupture life of DMWs with a range of axial loads and reduced weld angles (75°, 60°, 45° and 30°). The predicted results match reasonably well with the limited interface failure data for a 45° weld angle. This work also provides additional evidence and insights regarding the improvement of interface creep rupture life of DMWs in power plant pipelines, in particular: (1) Compared with a 45° weld angle, a 60° weld angle is more detrimental to the creep life and should be avoided in actual components – on the contrary, damage tolerance can be promoted by designing and adopting weld angles smaller than 45°, which can have lives exceeding that of standard 90° welded components; (2) A weld interface with alternating weld angles/paths is expected to enable a greater fraction of the creep rupture life to be taken up with crack propagation compared with a flat weld interface, which also increases the probability of damage detection; (3) A fully constrained boundary condition is beneficial to the creep rupture life compared with a free boundary condition; (4) For weld angles less than 90°, the diversion of the crack into the HAZ is less likely compared with a 90° weld angle. Type IV failure mode through the FGHAZ is also less likely to occur.

Creep–fatigue crack growth rate prediction based on fracture damage zone models

Based on a new fracture damage zone formulation and nonlinear elastic–plastic and creep crack tip fields, the prediction of creep–fatigue crack growth rate is studied. A unified crack growth rate equation is derived using the equivalent nonlinear stress intensity factor, monotonic low-cycle fatigue, and creep material properties at an elevated temperature. The crack growth rate model includes the size of the fracture process zone and damage parameters. The predicted creep–fatigue crack growth rates are compared with the experimental data of the 12Cr1MoV power plant steel and good agreement is observed.

A Stress-Strain Model for Unconfined Concrete in Compression considering the Size Effect

In this study, a stress-strain model for unconfined concrete with the consideration of the size effect was proposed. The compressive strength model that is based on the function of specimen width and aspect ratio was used for determining the maximum stress. In addition, in stress-strain relationship, a strain at the maximum stress was formulated as a function of compressive strength considering the size effect using the nonlinear regression analysis of data records compiled from a wide variety of specimens. The descending branch after the maximum stress was formulated with the consideration of the effect of decreasing area of fracture energy with the increase in equivalent diameter and aspect ratio of the specimen in the compression damage zone (CDZ) model. The key parameter for the slope of the descending branch was formulated as a function of equivalent diameter and aspect ratio of the specimen, concrete density, and compressive strength of concrete. Consequently, a rational stress-strain model for unconfined concrete was proposed. This model reflects trends that the maximum stress and strain at the peak stress decrease and the slope of the descending branch increases, when the equivalent diameter and aspect ratio of the specimen increase. The proposed model agrees well with the test results, irrespective of the compressive strength of concrete, concrete type, equivalent diameter, and aspect ratio of the specimen.

Simulation of Eccentric Impact of Square and Rectangular Composite Laminates Embedded with SMA.

In the present work, we study the low velocity impact, both central and eccentric, on square and rectangular laminated composite plates with embedded shape memory alloy (SMA) wires, which are stitched on the top and bottom surfaces of the plate, by using the finite element method. In finite element methods (FEM) simulations, a super-elastic SMA constitutive model is implemented in Abaqus/Explict by using a user defined material subroutine to describe the behaviors of SMAs. The three-dimensional (3D) Hashin failure criterion is adopted to model the damage initiation of laminated composite plates. To model the delamination failure, a cohesive damage zone model is introduced in interface elements. A comprehensive parametric study has been carried out to analyze the effects of eccentricity for the case of square and rectangular laminated composite plates.

Coupling damage and cohesive zone models with the Thick Level Set approach to fracture

This paper couples bulk damage modeling and cohesive zone modeling to get the benefits of both. Damage brings the directionality for the crack propagation as well as the possibility of crack branching while cohesive zone modeling allows for an explicit discrete crack modeling. The coupling is made easy through the Thick Level Set approach. The originality is that the coupling induces concurrent development of bulk and interface degradation.

A theoretical and computational framework for studying creep crack growth

In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the C^*-integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity hat{C}_k needs to be determined from the Finite Element analysis in terms of a dimensionless quantity phi _0, which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large phi _0, for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments.

Failure load prediction of laminates repaired with a scarf-bonded patch using the damage zone method

The damage zone method (DZM) is an efficient way to predict the failure of composite structures with a minimum of real testing. Particularly, it is useful when the failure mechanism is too complicated to be accurately analyzed by a merely numerical method. The aim of this study was to use the damage zone model to predict the failure load of repaired laminates, in which scarf-bonded joints were used for repair. The model uses a test-based critical damage zone and stress-based failure criteria. A total of 45 carbon-epoxy composite (USN) laminate scarf-repaired specimens were first tested with two different defect sizes, four scarf angles, and three overlap layer sizes. The Tsai-Wu and Tsai-Hill criteria were used for the laminate, and the maximum shear stress criterion for the adhesive was adopted to predict failure onset. The predicted failure loads were compared to test results and a good agreement was obtained with a 9.2% maximum deviation for almost all parameters with the exception of a case with an unrealistically large scarf angle. To verify the feasibility of the DZM for different material, additional 30 repair specimens using other unidirectional carbon-epoxy laminate were then also tested and the predictions were confirmed by the results of the experiment.

Tensile failure of laminates containing an embedded wrinkle; numerical and experimental study

The failure of a quasi-isotropic composite laminate containing an embedded out-of-plane fibre wrinkle defect was investigated under tension loading. Laboratory test specimens with controlled severity of fibre waviness were manufactured. Along with recording load–displacement data, high resolution camera images were taken at regular intervals which monitored the initiation and interaction of different damage mechanisms during test. Three-dimensional FE models were built following the geometry of actual test specimens. The information obtained from the tests was used to develop user material subroutines, implemented in Abaqus/Explicit as continuum damage and cohesive zone models for intra- and inter-ply failure respectively. The results of the simulations showed very good correlation with test observations in terms of failure load, location of damage initiation and interaction between different damage mechanisms for a range of waviness cases tested.

Compressive failure of laminates containing an embedded wrinkle; experimental and numerical study

An experimental and numerical study has been carried out to understand and predict the compressive failure performance of quasi-isotropic carbon–epoxy laminates with out-of-plane wrinkle defects. Test coupons with artificially induced fibre-wrinkling of varied severity were manufactured and tested. The wrinkles were seen to significantly reduce the pristine compressive strength of the laminates. High-speed video of the gauge section was taken during the test, which showed extensive damage localisation in the wrinkle region. 3D finite element (FE) simulations were carried out in Abaqus/Explicit with continuum damage and cohesive zone models incorporated to predict failure. The FE analyses captured the locations of damage and failure stress levels very well for a range of different wrinkle configurations. At lower wrinkle severities, the analyses predicted a failure mode of compressive fibre-failure, which changed to delamination at higher wrinkle angles. This was confirmed by the tests.

A discrete damage zone model for mixed-mode delamination of composites under high-cycle fatigue

A discrete damage zone model is developed to describe the mode-mix ratio and temperature dependent delamination of laminated composite materials under high cycle fatigue loading within the framework of the finite element method. In this approach, discrete nonlinear spring elements are placed at the finite element nodes of the laminate interface, and a combination of static and fatigue damage growth laws is used to define its constitutive behavior. The model is implemented in the commercial software Abaqus using the user element subroutine. The static damage model parameters are estimated from fracture mechanics principles, whereas the fatigue damage model parameters are calibrated by fitting the numerical results to published experimental data. A quadratic relation is proposed to describe the non-monotonic variation of fatigue damage model parameters with mode-mix ratio. Next, an Arrhenius relation is proposed for the temperature dependence of fatigue damage, in addition to the incorporation of the temperature dependence of critical fracture energy. The model is convergent upon mesh refinement; however, for accurate prediction the mesh size used for model calibration should be sufficiently small. The model predicted fatigue crack growth rates are in agreement with those obtained from a quadratic relation for the Paris law parameters for variable mode mix conditions, thus verifying the approach. While the model captures the temperature effects on delamination for mode I and 50 % mode II, our prediction deviates from experiments for pure mode II, since the corresponding damage mechanism entirely changes with temperature.

Progressive delamination analysis of composite materials using XFEM and a discrete damage zone model

The modeling of progressive delamination by means of a discrete damage zone model within the extended finite element method is investigated. This framework allows for both bulk and interface damage...

Simulations of ductile fracture in an idealized ship grounding scenario using phenomenological damage and cohesive zone models

Two complementary simulation methodologies for ductile fracture in large sheet metal components are presented and evaluated in this paper. The first approach is based on the phenomenological dilatational plasticity-damage model developed by Woelke and Abboud [46], which accounts for pressure-dependent volumetric damage growth through a scalar damage variable. The damage function represents phenomenologically micromechanical changes the material undergoes during the process of necking. Secondly, the cohesive zone model with an opening mode traction–separation law is employed to simulate the same ductile fracture problems accounting for significant variation of the multiaxial stress state along the crack path. Both methods are examined as to their capabilities to reproduce and predict the outcome of large-scale experimental fracture tests of welded and un-welded ductile plates subjected to large-scale penetration, simulating an idealized ship grounding. The results of the current study indicate that, with appropriate calibration, both approaches can be successfully employed to simulate ductile fracture in structural components under multiaxial stress. The advantages and shortcomings of each approach is discussed from the point of view of post-test numerical investigation as well as its predictive capabilities as an engineering tool.