Proposed Damage Model Research Articles

A void growth- and coalescence-dependent anisotropic damage model for polymeric foams

We present an elastic damage constitutive model for polymeric foam based on thermodynamics framework to consider the effects of anisotropy and the growth and coalescence of cavities. The evolution equation of the proposed model describes the material behavior sustaining anisotropic and unilateral damage. To carry out finite element analysis, the material properties for various polymeric foams are applied to the proposed damage model; we thus implement the proposed damage model in the commercial finite element program as a user-defined material subroutine. In order to validate the proposed anisotropic damage model, the numerical results are compared to the results of a series of tensile and compressive tests on various polymeric foams. Additionally, we propose the failure criterion for this damage model as based on the mass-dependent energy per unit mass at failure. The developed damage model can be used for further research on damage mechanics and finite element analysis of polymeric foams in continuum mechanics.

A novel continuum damage model to simulate quasi-brittle failure in mode I and mixed-mode conditions using a continuous or a continuous-discontinuous strategy

This paper formulated and implemented a novel local continuum damage model to be used with a continuous or a continuous-discontinuous strategy to simulate crack growth in quasi-brittle failure for mode I and mixed-mode conditions. The damage model is based on an evolution law using only physical parameters, which can be obtained through fracture and resistance tests without the need for further calibration. The local energy dissipation is controlled through regularization by the fracture energy and element length ensuring that different mesh densities dissipated the same energy during the damage evolution. The proposed damage model is employed in a finite element framework in two strategies: (i) a continuous strategy in which only the continuum damage model is used to predict crack propagation failure; and (ii) a continuous-discontinuous strategy in which a discontinuous enrichment is used to insert a crack within the elements after the total damage state is reached with no ad-hoc threshold value for the transition from continuous to the discontinuous approach. Comprehensive validation is demonstrated through comparisons with experimental results for various types of tests in mode I and mixed-mode conditions: single edge notch beam, unnotched four-point beam, anti-symmetric four-point shear beam, and double-edge-notched specimen. The results demonstrated that the proposed damage model and both strategies successfully simulated the crack propagation and failure of all simulated tests. Good agreement with the experimental results is observed for the crack path, maximum load, and entire load–displacement softening curves with coarser meshes than other models of the literature. Furthermore, the 3D results of the mixed-mode double-edge-notched specimen show that the proposed model provided good results even with coarser meshes using 16 times fewer elements than recent and similar results from the literature.

An anisotropic cohesive phase field model for quasi-brittle fractures in thin fibre-reinforced composites

Thin unidirectional-tape and woven-fabric composites are widely utilized in the aerospace and automotive industries due to their enhanced fatigue life and damage resistance. Providing high-fidelity simulations of intra-laminar damage in such laminates is a challenging task both from a physics and a computational standpoint, due to their complex and largely quasi-brittle fracture response. This is manifested by matrix cracking and fibre breakage, which result in a sudden loss of strength with minimum crack openings; subsequent fibre pull-outs result in a further, although gradual, strength loss. To effectively model this response, it is necessary to account for the cohesive forces evolving within the fracture process zone. Furthermore, the interaction of the failure mechanisms pertinent to both the fibres and the matrix necessitate the definition of anisotropic damage models.We propose a cohesive phase-field model to simulate intra-laminar fracture in fibre reinforced composites. To capture damage anisotropy, distinct energetic crack driving forces are defined for each pertinent composite damage mode together with a structural tensor that accounts for material orientation dependent fracture properties. The material degradation is governed by a 3-parameter quasi-quadratic degradation function, which can be calibrated to experimentally derived strain softening curves. The proposed damage model is implemented in Abaqus and is validated against experimental results.

Forming Limit Prediction of Anisotropic Aluminum Magnesium Alloy Sheet AA5052-H32 Using Micromechanical Damage Model

This paper focuses on the implementation and applicable evaluation of a modified Gurson–Tvergaard–Needleman (GTN) damage model for predicting forming limit diagram of anisotropic aluminum alloy sheet, in which its elasto-plastic behavior is assumed to obey a non-quadratic anisotropic yield criterion. The original porous ductile material model is heuristically enhanced to suit anisotropy of sheet metal, and then, it is implemented via a user material subroutine using finite element codes of ABAQUS/Explicit software package. The material damage model is calibrated and applied to predict forming limit diagram of commercial aluminum alloy sheet AA5052-H32 via the Nakajima drawing tests under plane stress condition. To obtain various strain paths, the Nakajima tests are conducted for seven specimens, which are designed in accordance with standard ISO 12004-2-2008. The influence of material anisotropy on the predicted forming limit is also considered and discussed. The numerical simulation results obtained from the proposed damage model showed a good agreement with those of the experimental data.

An Ordinary State-Based Peridynamic Model for Fatigue Cracking of Ferrite and Pearlite Wheel Material

To deal with a new-developed ferrite and pearlite wheel material named D1, an alternative ordinary state-based peridynamic model for fatigue cracking is introduced due to cyclic loading. The proposed damage model communicates across the microcrack initiation to the macrocrack growth and does not require additional criteria. Model parameters are verified from experimental data. Each bond in the deformed material configuration is built as a fatigue specimen subjected to variable amplitude loading. Fatigue crack initiation and crack growth developed naturally over many loading cycles, which is controlled by the parameter “node damage” within a region of finite radius. Critical damage factors are also imposed to improve efficiency and stability for the fatigue model. Based on the improved adaptive dynamic relaxation method, the static solution is obtained in every loading cycle. Convergence analysis is presented in smooth fatigue specimens at different loading levels. Experimental results show that the proposed peridynamic fatigue model captures the crack sensitive location well without extra criteria and the fatigue life obtained from the simulation has a good correlation with the experimental results.

Simplified damage models for circular section reinforced concrete bridge columns

Damage models are fundamental elements within probabilistic frameworks, such as Performance-Based Earthquake Engineering (PBEE), for the seismic assessment of RC structures. For bridges, in specific, there are not many available experimental results for the characterization of damage in the RC columns hence the numerical counterpart acquires particular relevance. In this paper, via Monte Carlo simulation and comparison with complementary experimental results, a damage model consisting of a library of median and logarithmic dispersion values for curvature ductility, displacement ductility and drift, describing the probability of reaching a particular damage limit state are generated as a function of key parameters of circular RC bridge columns. Four damage limit states are considered: slight, moderate, extensive and complete. Simplified relationships based on the full datasets are proposed for easier implementation. The proposed damage models can be used for threshold identification and economic loss assessment in performance-based earthquake engineering of RC bridges.

A modified Bonora damage model for temperature and strain rate-dependent materials in hot forging process

The initiation and propagation of damage are sensitive to temperature and strain rate, especially for ultra-super-critical rotor steel with high strength at elevated temperature, which probably leads to premature failure in the hot forming process. To accurately describe the damage behavior, a novel damage model incorporating temperature and strain rate was proposed based on Bonora damage model. To establish this damage model, a GA (genetic algorithm)-based inverse method was designed for identifying four damage parameters in Bonora damage model by correlating experimental and simulation data in the tensile tests at elevated temperatures and different strain rates. And then these damage parameters as functions of temperature and strain rate were determined. The proposed damage model was integrated into a finite element software FORGE to simulate the damage evolution of a notched upsetting specimen and the hot tensile specimens. The damage from compressive to tensile states and the fracture behavior were properly predicted, respectively. Additionally, the digital image correlation (DIC) technique was employed to capture the crack initiation and propagation on a flate notched X12 ultra-super-critical rotor steel specimen, which were compared with simulation results to further verify the accuracy of the proposed damage model.

Capability analysis of Puck damage model in predicting the damage behavior of unidirectional composite laminates under different scenarios

Composite materials have been broadly used in many engineering fields because of their distinctive properties. They have advantages over metals as their properties offer significant advantages such as very good strength to weight ratio. However, failure in composite structures due to interlaminar and intralaminar raises a maintenance concern because it can lead to invisible damage. Therefore, this paper presents the capability of three-dimensional Puck failure criteria with gradual degradation rule to predict the structural responses, as well as the onset and propagation of failure due to variation of the situation in a composite laminate. The proposed damage model is achieved via the implementation of user-subroutines both in statics and explicit analysis using Abaqus software. Three different scenarios are investigated which were open-hole tension, low-velocity impact, and multi-bolt double-lap joint. The force-displacement and force-time curves are recorded and compared with experimental data taken from literature to measure the performance of such damage model. It is found out that the model adopted here responses well with test curves and demonstrates the high capability of predicting the damage in the direction of in-plane and out-of-plane in a composite laminate.

A damage model to evaluate the mechanical properties in the medium-long life stage for coating system subjected to elevated thermal loads with 3D-DIC technique

Abstract Various damage models were proposed to quantify the life of TBCs subjected to elevated thermal exposure loads, which are of great engineering significance, but they can not achieve satisfactory life prediction accuracy in the medium-long life stages, and also can not distinguish the additional damage caused by thermal cycle. In this paper, based on the 3D-DIC technique, the spalling strain of the coating system under different thermal treatments was obtained, and it can be used as a parameter to quantify the damage of the coatings. Based on the above work, a damage model was developed, which can not only model the damage evolution of coatings but also describe the additional damage introduced by thermal cyclic behavior. Based on the proposed damage model, this paper discussed the life prediction accuracy of coatings in the medium-long life stages and compared the weight method, thickness method and the method proposed in this paper. The results show that the proposed method based on the spalling strain as the damage parameter is of great significance to improve the life prediction accuracy of coatings in the medium-long life stages.

Damage analysis of RC tall building structures under earthquake loading

A Practical 1D cyclic model for concrete is established. The model is a combination between the skeleton curves in Chinese Concrete Code (GB50010-2010) and the modified hysteretic rule in Yassin model. The cyclic model has the tensile and compress damage variables which are able to depict the damage of concrete. The present model is developed as a user material subroutine VUMAT in ABAQUS. Then, the damage evolution analysis of a RC tall building structure was performed by the proposed damage model and the built-in damage model for concrete in ABAQUS. The results show that the cyclic model is suitable for the damage evolution and pattern analysis of RC tall building structures under earthquake loading.

A new damage model accounting the effect of joint orientation for the jointed rock mass

Damage accumulation in the rock mass leading to failure is influenced by the properties of pre-existing discontinuities. In order to simulate rock mass behaviour realistically, many damage models have been proposed. Amongst them, limited damage models consider joint orientation, one of the significant properties of discontinuities impacting the rock mass failure, in the strongly anisotropic rock masses. In this study, we propose a statistical damage model using the Weibull distribution which takes into account joint orientation by incorporating the Jaeger’s and modified Hoek-Brown failure criteria for jointed rock masses. The proposed statistical damage model is validated using experimental results. Furthermore, verification of the proposed model is conducted by distinct element method using Particle Flow Code (PFC). To investigate the influence of the shape parameter (m) and scale parameter (F0) of the Weibull distribution on the statistical damage model predictions, a sensitivity analysis is carried out. It is found that the parameter m only depends on strain parameter k. On the other hand, the parameter F0 is indirectly related to the failure strength of the jointed rock mass in the proposed damage model. Considerable influence of joint stiffness on the damage variable D, damage evolution rate Dr and rock mass responses are also identified.

A nonlinear damage creep model for sandstone based on fractional theory

In this study, an improved viscoelastic model is proposed, which is based on the application of Caputo fractional derivatives of one function in regard to exponential function. This new mathematical way is effective in the construction of viscoelastic model with time dependence. And based on the type of Norton power law and damage factor, we propose a new damage model. By combining the improved viscoelastic model and proposed damage model, a nonlinear fractional damage creep model is presented to describe the creep mechanical behavior of sandstone. A series of creep experiments were conducted on the sandstone by the step loading way. The decaying, steady, and accelerating creep stage all appear in the experiments. Based on those experimental data, the fitting curves of the presented creep model are in well agreement with those of the experimental data. And the reasonability of fitting parameters also has been analyzed in detail.

Online multiaxial fatigue damage evaluation method by real‐time cycle counting and energy‐based critical plane criterion

AbstractTo realize online multiaxial fatigue damage assessment for the mechanical components in service, an online multiaxial cycle counting method is proposed coupled with the segment processing technique and Wang‐Brow's relative equivalent strain concept. Meanwhile, considering all the stress and strain components, which contribute to the fatigue damage on the critical plane, a multiaxial fatigue damage model without any weight coefficients is also proposed in an equivalent form of shear strain energy. Then, an online fatigue damage evaluation method for multiaxial random loading is developed by combining with the proposed damage model and online cycle counting method. The experimental results showed that the proposed online cycle counting method can be successfully applied to the calculation of multiaxial fatigue damage under random loading. Moreover, the proposed online multiaxial fatigue damage evaluation method can provide satisfactory predictions.

Experimental investigation and damage simulation of large-scaled filament wound composite pipes

This paper investigates the progressive collapse of filament wound Toray T700/Epotech X4201 composite pipes with various layups via a combined experimental and numerical study. The experimental program examines the flexural behavior of full-diameter T700/X4201 pipes under four-point bending and the tensile behavior of filament wound coupon specimens cut from the pipes. The tests show that the composite layup significantly influences the deformation, flexural resistance, and failure mechanisms of the composite pipes. The CFRP pipe with the optimal complex layup [(90/±15/90/±453)5/±453] design has higher ultimate resistance in bending than other designs with layups of [±45]28 and [90]56. Coupon tests show similar effects of composite layup on the tensile behavior of coupon specimens. The numerical effort evolves a three-dimensional progressive damage model to predict the failure in the CFRP coupons and pipes. The damage model incorporates a nonlinear in-plane shear behavior of the T700/X4201 composite material prior to damage initiation and uses a continuum damage mechanics approach to model the matrix and fiber damage progression in the composite pipes. The combined experimental-numerical work provides a more complete understanding of the bending behavior of large-scaled composite pipes, showing distinct failure modes for filament wound pipes with different layups. The load-displacement curves, ultimate bending resistance and failure modes of the composite pipes with different layups are accurately captured using the proposed damage model, demonstrating the capability for the failure analysis of large-scaled composite pipes such as composite risers in offshore applications.

DAMAGE MODEL CALIBRATION FOR S275 AND S690 STEELS

AbstractA calibration procedure for material damage models of S275 and S690 structural steels is proposed based on their full range engineering stress‐strain curves. Combined linear and power stress‐strain laws with a weighting factor are used to describe damaged stress‐strain relations after necking. Material damage models are proposed based on the estimation of undamaged stress. Tensile coupon tests on S275 and S690 steels are modelled in ABAQUS with the explicit solver. Results show that the numerical engineering stress‐strain curves based on the proposed damage models are very close to the experimental results. An investigation is made to establish the damage susceptibility for S275 and S690 steels.

Development of an impact damage model for medium and large scale composite laminates using stacked-shell modeling: Verification and experimental validation

In the present work, the predictive capabilities of a Finite Element (FE) damage model developed for accurate and efficient analysis of medium to large scale structures are investigated. The proposed damage model is based on stacked sublaminate modeling approaches with cohesive interfaces. A pre-failure elastic response verification procedure is followed by model validation, performed by a Mode-I fracture toughness experimental campaign, from which the model predictive capabilities in interlaminar damage initiation and propagation are assessed. The analysis is then extended to the simulation of low velocity impact experiments found in the open literature, investigating the capabilities of the proposed model in intralaminar and interlaminar damage prediction. The results demonstrate the proposed methodology’s accuracy and efficiency in the simulation of laminated composites under static and impact conditions.

Effects of uniaxial and triaxial compression tests on the frozen sandstone combining with CT scanning

To explore the mechanical properties of frozen sandstone, the medical X-ray and self-designed triaxial equipment were applied to conduct the real-time uniaxial and triaxial compression scanning tests at room temperature of 20°C and different freezing temperatures of −2°C, −6°C and −10°C. Moreover, computed tomography (CT) scanning images of dry sandstone samples, saturated sandstone samples and saturated frozen sandstone samples were employed to compare and analyse their mechanical features. On the basis of the stress–strain curves and CT scanning images of frozen sandstone samples under different stress states, the influences of confining pressure and freezing temperature on the mechanical properties of frozen sandstone are explored, and the relationships between the average CT value and its variance of the three selected regions and the corresponding stress states are also analysed. In addition, a new damage variable of frozen sandstone based on the volume mean and variance of CT values of the whole sample is proposed to consider the evolving meso-structures in the loading process, and a damage constitutive model for frozen sandstone under uniaxial compression conditions is also formulated. Finally, comparing the experimental results with theoretical ones, the proposed damage model is verified to be capable of describing the stress–strain relationship of frozen sandstone.

Characterization of electric-field enhancement leading to circuit-layout dependent damage of low-k films when exposed to processing plasma

We investigated the effects of Cu-line layouts on plasma-induced radiation damage (PRD) to interline low-k dielectric films. We carried out a finite-element-method-based three-dimensional (3D) electromagnetic simulation (EMS), in which a Drude free-electron model was implemented for the dielectric function of Cu lines. The 3D EMS analysis revealed that the electric field in the low-k films was enhanced for specific Cu-line layouts exposed to N2 plasma irradiation, while no clear electric-field enhancement was observed for Ar plasma exposure. The specific optical emission lines produced in N2 plasmas are the root cause of damage creation in the low-k dielectric films with embedded Cu lines. The 3D EMS analysis predicted that the electric field was enhanced with decreasing the line and space (L/S) widths. The prediction implies that the Cu-line-layout dependent PRD should be more prominent as device dimensions shrink. We verified the predicted results experimentally using devices with low-k films between various L/S Cu lines, in addition to a blanket wafer—without Cu lines. We found that an increasing peak in the low-k dielectric constant appeared at a specific L/S width after N2 plasma exposure and no clear increase in the dielectric constant was observed after Ar plasma exposure. The obtained experimental results are consistent with the 3D EMS analysis. We propose a damage model, where the electric field enhancement plays an important role in the low-k dielectric films with embedded Cu lines. The proposed damage model is indispensable for minimizing PRD and designing Cu layouts in future devices.

Load-resistance analysis: an alternative approach to tsunami damage assessment applied to the 2011 Great East Japan tsunami

Abstract. Tsunami fragility functions describe the probability of structural damage due to tsunami flow characteristics. Fragility functions developed from past tsunami events (e.g., the 2004 Indian Ocean tsunami) are often applied directly, without modification, to other areas at risk of tsunami for the purpose of damage and loss estimations. Consequentially, estimates carry uncertainty due to disparities in construction standards and coastal morphology between the specific region for which the fragility functions were originally derived and the region where they are being used. The main objective of this study is to provide an alternative approach to assessing tsunami damage, especially for buildings in regions where previously developed fragility functions do not exist. A damage assessment model is proposed in this study, where load-resistance analysis is performed for each building by evaluating hydrodynamic forces, buoyancies and debris impacts and comparing them to the resistance forces of each building. Numerical simulation was performed in this study to reproduce the 2011 Great East Japan tsunami in Ishinomaki, which is chosen as a study site. Flow depths and velocities were calculated for approximately 20 000 wooden buildings in Ishinomaki. Similarly, resistance forces (lateral and vertical) are estimated for each of these buildings. The buildings are then evaluated for their potential of collapsing. Results from this study reflect a higher accuracy in predicting building collapse when using the proposed load-resistance analysis, as compared to previously developed fragility functions in the same study area. Damage is also observed to have likely occurred before flow depth and velocity reach maximum values. With the above considerations, the proposed damage model might well be an alternative for building damage assessments in areas that have yet to be affected by modern tsunami events.

Interior induced fatigue of surface‐strengthened steel under constant and variable loading: Failure mechanism and damage modeling

AbstractPulsating tension tests with constant amplitude (CA) and variable amplitude (VA) were conducted to investigate the interior failure mechanisms of a carburized Cr steel, and a cumulative damage model with the fine granular area (FGA) formation process was proposed in this study. Such a steel represents the continuously descending S‐N (stress‐number of cycles) curve characteristics associated with inclusion‐FGA‐fisheye induced failure even under variable amplitude. Due to crack growth retardations and accelerations resulted from the interaction effect between stepwise resets of the applied stress, the crack morphology under variable amplitude loading is much rougher. The interior failure mechanism was elucidated in combination with the determination of stress intensity factor values at different crack tips. Based on proposed damage model, the agreement between the predicted and experimental results is fairly good within the factor‐of‐two range.