Modified Damage Model Research Articles

Modified Damage Model of Aeolian Sand Self-Compacting Concrete

Modified Damage Model of Aeolian Sand Self-Compacting Concrete

Influence of earthquake duration on structural collapse capacity: Application to self-centering shear walls

This study investigates the influence of earthquake duration on the structural collapse capacity of self-centering shear walls (SCSW). The assessment process employing different response indicators is examined when considering the duration effect, including the inter-story drift ratio (IDR) and damage index (DI) quantified through a modified damage model. SCSWs with varying self-centering parameters λ are designed and modeled, and incremental dynamic analyses are performed using two record sets with distinct effective durations and equivalent frequency contents. The assessment criteria outlined in FEMA P695 are utilized to quantify the collapse capacity of SCSWs considering the duration effect. Meanwhile, the duration effect on structural performance corresponding to multiple damage states are evaluated. Results show a minimal correlation between the duration effect and collapse capacity when employing IDR during evaluations. Conversely, earthquakes with longer durations may impose higher collapse risks to SCSWs when assessing collapse capacity using DI. Meanwhile, enlarging λ can effectively mitigate damage development and reduce collapse risks for SCSWs. The results further demonstrate that damage may develop more rapidly within SCSWs under long-duration earthquakes, potentially leading to inadequate redundancy during intense seismic events. Additionally, the result suggests that the current performance assessment process only employing deformation-based response indicators may lead to inadequate evaluation of collapse risks for SCSWs, especially when accounting for the effect of earthquake duration.

Nonlinear stress growth and failure characteristics of gangue-cemented backfill

The stability of a filling body is the main control index of the filling effect, which is significantly affected by the strength and damage characteristics, and its stress increases nonlinearly with damage evolution. In this study, the uniaxial compression test and digital image correlation (DIC) method were used to investigate the stress and damage characteristics of a gangue-cemented backfill, and the stress–strain characteristics and crack propagation laws of the backfill under different curing ages were analyzed. A modified damage model of the gangue-cemented backfill based on the Weibull distribution characteristics of the microelement damage of the backfill and pore closure characteristics in the compression stage was constructed. Through numerical simulations, the nonlinear growth characteristics of stress in the specimen were revealed from the perspective of energy dissipation. The results showed that the nonlinear increase in stress originated mainly from pore closure and crack extension. The crack propagation in the backfill was divided into intermediate crack budding and symmetric crack propagation at the corners. The key signs of the peak stress and fracture of the specimen are the connection of the surface cracks and fracture surfaces on both sides. The proposed modified damage model was proven to be in relatively close agreement with the experimental results. The stress growth in the backfill exhibited a nonlinear-linear-nonlinear growth pattern before the peak stress. This study provides a theoretical basis for studying the strength characteristics and damage evolution of backfill, which is important for optimizing the material proportions and analyzing the stability of the quarry and other aspects.

Investigation of the High-Temperature Low-Cycle fatigue failure characteristics of P91 steel weld joints and their fatigue strength reduction factors under various load control regimes

Low cycle fatigue tests are conducted on the base metal, weld metal, a welded joint under the condition that the strain control region is the joint (WJWJ) and a welded joint under the condition that the strain control region is the base metal (WJBM) of P91 steel at 500℃ using different total strain ranges. The cyclic stress response is highest for the weld metal, followed by the base metal, and is relatively similar for WJWJ and WJBM. At 2.0 % total strain range conditions, the materials generally exhibit non-Masing behavior and dynamic strain hardening aging. At all total strain ranges, WJWJ failed in the heat-affected zone, and WJBM broke in the base metal. For the difference in fatigue life between base metal and welded joints, the fatigue strength reduction factor of P91 steel welded joints at 500 °C is given as a suggested value. The fatigue behavior of P91 steel welded joints is verified based on a hybrid hardening model and a modified damage model. This study presents a theoretical framework for analyzing the fatigue strength reduction factors of weldments and comparatively analyzes the effects of different geometrical features.

Peridynamic modelling of dynamic damage and fragmentation of cracked solids during impact contact

Dynamics damage of solids exhibit unique characteristics that are absent in static analysis. The presence of pre-existing cracks further increases the complications. To address this issue, the present study focuses on modelling dynamic damage of cracked solids during impact contact. The model is formulated based on the state-based peridynamics. It incorporates a modified damage model and employs the short-range force approach to capture the impact damage. The damping force is introduced to eliminate numerical oscillation around cracks. Then, the adaptive explicit time integration is introduced to efficiently solve the peridynamic equations. Model performance is evaluated through benchmark tests. Next, we simulate impact between two spheres with pre-existing cracks. Our focus lies in comprehending the mechanisms by which material properties and crack patterns affect damage. Further sensitivity analysis reveals that the kinetic energy of the impact system is significantly affected by the pre-existing cracks and geometric parameters of the cracks, including their number, length, angle, and distribution. The interplay of crack interaction and the gradual connection of the damaged region plays a vital role in the phenomena. The presented study offers insights into damage evolution during impact contact and provides guidelines for assessing impact damage in structures with pre-existing defects.

Prediction of the irradiation effect on the fracture toughness for stainless steel using a stress-modified fracture strain model

This paper proposes a numerical method for predicting the reduction in the fracture toughness with neutron dose using the concept of an embrittlement constant. Tensile and fracture toughness test data for type 304 stainless steel in the literature [41,42] are used to validate the proposed method. Fracture toughness tests are simulated using a stress-modified fracture strain damage model implemented in an ABAQUS user-subroutine. The true stress-strain curve and one point of the fracture strain locus are obtained from the tensile test simulation. The remaining parameters of the fracture strain locus are determined by simulating a fracture toughness test. The fracture strain locus is modified to reflect the irradiation effect on the fracture toughness using the proposed irradiation embrittlement constant CI. The function of the constant with the neutron dose is calculated from the tensile tests and simulations. Subsequently, the modified damage model is used to predict the reduction in the fracture toughness. The predicted simulation results are compared with experimental data, showing good agreement.

Performance-based damage quantification and evaluation for self-centering concrete frames

Self-centering concrete frames (SCCFs) are designed to provide superior seismic capacities with resilient features. Although a well-designed SCCF can limit damage development, it still impairs post-earthquake performance and shall be considered properly. Quantifying and evaluating structural damage can provide valuable guidance for seismic designs and post-earthquake assessments, yet related studies towards SCCFs are still limited. This paper aims to conduct damage quantification and evaluation for SCCFs. The damage development and distribution within SCCFs are investigated. A modified damage model is adopted to quantify the damage developed in beam-column joints. Weighting coefficients based on the hysteretic energy demands are introduced to assess story and integral structural damage. 12 SCCFs with different structural features are designed and analyzed under 44 ground motions. The damage development within structures is quantified and evaluated using the performance-based damage intervals. The results show that damage developed in SCCFs exhibit stable growth with seismic intensities, implying superiorities in the damage controllability and stability. Meanwhile, increasing the self-centering parameter λ proves effective in reducing damage developed in SCCFs. A method to estimate integral structural damage is proposed, while proper design parameters are suggested to further assist seismic designs for SCCFs based on analytical results.

Comparison of deformation behavior between creep and fatigue on siltstone and its modified damage model

AbstractIn order to reveal the deformation behavior similarity between creep and fatigue, a series of creep and cyclic load tests were performed on siltstone under various load levels. First, the mechanical characteristics of creep and fatigue were compared, by analyzing the strength, ultimate strain, and steady deformation rate of siltstone. Then, a modified fatigue damage creep model was established by connecting a viscoplastic damage element in series with Burgers mode. Finally, the applicability of the model was verified, and the model parameters were analyzed. The results show that the fatigue failure of siltstone is controlled by fatigue strength and limit strain. The modified fatigue damage creep model can accurately describe the whole deformation process of siltstone under cyclic load test. Compared with creep test, the cyclic load hardly affects the elastic modulus of this model. However, the viscosity coefficient of this model is greatly weakened by the cyclic load.

A Hybrid Method for Predicting Fatigue Life of Lead-Free Solder Joints Under Coupled Electrical–Thermal–Mechanical Fields

A hybrid method was developed in this study for fatigue life prediction (FLP) of lead-free solder (LFS) joints in ball grid array package under the coupled electrical–thermal–mechanical (ETM) fields. A modified constitutive model for lead-free solder joints under coupled ETM fields was proposed to describe the mechanical and fatigue behavior of solder joints under coupled ETM fields. A modified damage model under coupled ETM fields was then developed to obtain the fatigue life of LFS joints under coupled ETM fields. Uniaxial tension tests of an Sn–3.0Ag–0.5Cu (SAC305) solders and coupled multifields fatigue experiments were performed to verify the accuracy, applicability and validity by the modified constitutive model and fatigue damage model under coupled ETM fields. Based on the modified constitutive model and fatigue damage model, a hybrid method, including current, temperature and mechanics parameters, was proposed for the FLP of the LFS joints, which was demonstrated to be able to predict the results well. A hybrid method provides an idea for investigating the fatigue life of lead-free solder joints in coupled fields.

A modified fatigue damage model considering loading sequence effect

A modified fatigue damage model is proposed considering the loading sequence effect under variable amplitude loading conditions. The transition sequence is obtained from the counting sequence by an equivalent rainflow counting method and is used to provide the loading sequence information for fatigue damage accumulation prediction. Rainflow counting matrix and sequence transition matrix are formulated based on the rainflow counting sequence and the transition sequence. The relation between the two matrices and the original loading sequence is evaluated in detail. In the deterministic fatigue estimation, the rainflow counting matrix and the sequence transition matrix are integrated into the proposed modified damage model based on the linear damage rule. Mean stress transition is applied to the rainflow counting matrix for loading level effect. Existing experimental data are used to validate the fatigue damage estimation from the deterministic framework. In order to evaluate the fatigue under random loading conditions, the rainflow counting matrix and sequence transition matrix are mapped to one-dimensional exponential and Laplace distributions based on the stationary random process. Numerical simulation is conducted to validate the proposed mapping distributions. Meanwhile, the impact of the correlation length on the proposed distributions under stationary random loading sequence is investigated as well. Finally, with the given distributions of the rainflow counting matrix and sequence transition matrix, a reconstruction procedure is simulated and discussed for probabilistic fatigue estimation. The proposed model provides a sophisticated approximation to the original loading sequence with a sequence transition effect. The proposed modified fatigue damage model corrects the deficiencies of the linear damage rule with sufficient sequence information from the originally applied loading. Furthermore, the probabilistic fatigue estimation can evaluate the accumulated fatigue damages under a random loading process with the sequence transition effect.

Damage and quantitative indexes for steel reinforced concrete column with T-shaped section

This paper presents an experimental investigation on damage performance of nine steel reinforced concrete (SRC) columns with T-shaped section under different loading paths. The monotonic loading, low cyclic reversed loading and mixed loading were applied to specimens along the flange of specimen. Furthermore, different axial compression ratios and steel ratios were used to study the damage of specimen. The failure modes were observed and the load-displacement curves were analyzed. The results indicate that the specimens mainly showed the feature of bending failure accompanied by bond failure characteristic at the end of loading. The load-displacement curve was plump and symmetrical without obvious pinch under the low cyclic reversed loading. The ductility coefficient lied within the range of 5.34–9.41, which indicates that these columns had better deformation capability. Based on the experimental results, a modified damage model considering deformation and energy dissipation was proposed, where the effects of concrete cracking, loading path and effective energy dissipation on damage were studied. Moreover, the damage index at each loading stage was calculated. Meanwhile, the level of seismic performance of SRC T-shaped column was divided into five levels, namely the normal use, the basic normal use, the temporary use, the post-repair use, and the near serious damage. Many SRC T-shaped columns were chosen as the analysis samples to obtain the displacement angles under different loading stages. Based on statistic results, the corresponding relationship between quantitative index of displacement angle and the damage index was established.

A modified Mazars damage model with energy regularization

This paper presents a modified Mazars damage model, based on a strain formulation, for the physically nonlinear analysis of concrete structures. The main objective is to propose a modified damage model, in which both tension and compression damage evolution laws are regularized using a classical fracture energy methodology. The original loading functions are maintained, including their thermodynamic consistencies. The most relevant modification of the model is introduced in the damage evolutions laws, which are updated in order to produce similar stress–strain relations to those presented in fib Model Code 2010. The softening branch under both compressive and tensile strains is regularized with fracture energy. The damage model is then benchmarked with classical experimental and numerical tests considering monotonic loadings. The new constitutive relation was implemented in the commercial software ABAQUS via user subroutine UMAT. Research needs towards a definition of a generalized damage model with energy regularization are discussed and presented.

Multiaxial fatigue behavior of SLM Ti6Al4V alloy under different loading conditions

AbstractThe multiaxial fatigue behavior of Ti6Al4V samples, made by selective laser melting (SLM) process, was investigated in this work. Fatigue tests were carried out under three different loading conditions: (i) tensile, (ii) torsion, and (iii) in‐phase axial–torsional. A modified damage model, based on the Sines criterion, is proposed and used to analyze proportional multiaxial fatigue data. Preliminary results showed that the proposed version provides a better prediction with respect to the Sines model. Infrared thermography and digital image correlation were also used to capture both temperature and strain evolutions during fatigue tests. Fatigue results highlighted different failure modes due to surface crack initiation and internal crack initiation, as also demonstrated by scanning electron microscopy of the fracture surface.

Life assessment of a low-alloy martensitic steel under isothermal low-cycle fatigue-creep and thermo-mechanical fatigue-creep loading conditions

Strain-controlled Low-Cycle Fatigue tests (LCF) and Thermo-Mechanical Fatigue tests (TMF) were performed on a low-alloy martensitic steel in the temperature range between 300 °C and 600 °C, with and without a strain dwell. TMF tests were performed for three different phase angles between thermal strain and mechanical strain: as in-phase, as out-of-phase and as counter clockwise-diamond. The results show that the phase angle that is employed has a significant influence on the dominant damage mechanism and on the observed lifetime. Finally, a modified damage model is proposed in order to take into account the effect of the phase angle.

Creep rupture mechanism and microstructure evolution around film-cooling holes in nickel-based single crystal superalloy specimen

The fracture mechanism and microstructure evolution around film-cooling holes in a nickel-based single crystal superalloy specimen under tensile creep at high temperatures were investigated using thin-walled plate specimens with close-packed film-cooling holes. The results demonstrated that the film-cooling hole structure has a weakening effect on the specimen for the creep life and creep ductility. In the specimen with the film-cooling holes, a large number of small cracks formed from initial cracks along the direction of the maximum resolved shear stress during the high-temperature creep process, and the cracks propagated along the direction perpendicular to the loading stress direction. Further, the microstructure evolution of the γ′ phase around the edge of the film-cooling holes was closely related to the local stress. While N-type rafting occurred in the high-stress zone, no significant change of microstructure was observed in the low-stress zone. Further, a modified damage model of the crystal plasticity theory was used to simulate the deformation of the specimen with cooling holes under multi-axial stress state, and the results of finite element analysis (FEA) agreed with both the test results and fracture morphology.

Experimental Study and Damage Model Study of Rock Salt Subjected to Cyclic Loading and Cyclic Creep

Due to the gas injection and production of underground salt caves during the operational phase, rock salt is often subjected to a combined stress of cyclic pressure and constant pressure. In order to investigate the damage evolution of rock salt under different combined stresses, the uniaxial cyclic loading test and cyclic creep test were carried out. The stress‐strain curves, energy characteristics, energy dissipation, and damage of rock salt in the two experiments were analyzed and compared. The test results show that the stress‐strain curves of the two tests presented three stages of “sparse”‐“dense”‐“sparse.” As the maximum stress increases, the stage of “dense” will decrease and the rock salt cycle life will decrease. The relationship between cycle life and Δσ (difference between maximum and minimum stress in the tests) is an exponential function under cyclic loading and a linear relationship under cyclic creep. Based on the experimental data, the energy dissipation of rock salt is analyzed. The damage variables were defined from the perspective of energy dissipation, and the damage evolution of rock salt under two tests was obtained. There are three corresponding stages of energy dissipation and damage: initial, constant speed, and acceleration. The damage model is obtained by inverse functioning the s function, and then the correction coefficient is added to the model to obtain the modified damage model. The modified damage model is compared with the experimental data. The results show that the model can accurately describe the three stages of rock salt damage. The significance of parameters in the modifying damage model is also discussed.

Quantitative Damage and Fracture Mode of Sandstone under Uniaxial Load Based on Acoustic Emission

The damage degree and fracture mechanism of the rock are important to the bearing performance of the rock mass and the stability of the overlying structure. Most of the existing damage models for characterizing rock damage exclude the range of postpeak stress or do not consider the compaction and closure stage of the fracture, and the description of the quantitative damage of sandstone is not accurate enough. In addition, the description of the rock fracture mechanism under load is not exact enough. Aiming at the problem of quantitative damage and fracture mechanism of the loaded rock, this paper adopts acoustic emission (AE) to monitor the loading process of sandstone under uniaxial loading. In accordance with the characteristics of the AE signal, the loading stage of sandstone under uniaxial load is divided into three stages: initial hit stage, hit stability stage, and hit instability stage. By modifying the traditional damage model and combining the AE signals of the sandstone under the load, a modified damage mechanics model is obtained, which can fully express the entire loading stage. Furthermore, through the analysis of AE signals, the fracture mechanism of sandstone under uniaxial load is studied. The results show that the modified damage model can quantitatively describe the damage at different loading stages which include two areas including the fracture compaction closure stage and the postpeak stress stage. The failure and instability of sandstone under uniaxial load is mainly shear failure. The research results can provide a reference for the nondestructive testing of sandstone and engineering reliability in geotechnical engineering.

A void evolution-based damage model for ductile fracture of metallic materials

A modified damage model is developed for describing ductile fracture of metallic materials by introducing damage variables with respect to porosity. Based on the geometric characteristics of the void deformation process, modified governing equations of void evolution are proposed to reduce the dependence of micro parameters. A transformed variable is introduced to incorporate the porosity into continuum damage mechanics. The numerical predictions are compared with experimental results for AISI-1095, AISI-1090 and AISI-1045 steel.

Damage Constitutive Model Based on Energy Dissipation for Frozen Sandstone Under Triaxial Compression Revealed by X-Ray Tomography

A series of triaxial compression tests, with real-time computed tomography (CT) scanning performed in the loading process, were conducted on frozen sandstones at confining pressures of 0, 1, 2, and 3 MPa at different temperatures of −2, −6, −10, and 20 °C, respectively. The experimental results indicate that the strength of frozen sandstone increases with a decrease in temperature. The strength of frozen sandstone increases with an increase in the confining pressure at freezing temperatures. In the loading process, the evolution law of the CT value of the whole sandstone is explored, and three-dimensional reconstruction of CT images, which denote postfailure models of frozen sandstone, is also performed. According to energy dissipation theory, an isotropic damage variable is introduced. Based on the CT value of the whole sandstone, the concept of the compaction coefficient K, which describes the compaction degree, is proposed to modify the damage model obtained by Lemaitre’s strain equivalence hypothesis. The validity of the model is verified by comparing its computed results with the experimental results obtained from triaxial compression tests. The results indicated that the modified damage model can adequately predict the stress-strain relationship of the frozen sandstone.

Probabilistic seismic demand model for regular bridges based on the modified Park-Ang damage index

In this paper, a modified damage model is established to solve the non-convergence problem existing in the Park-Ang damage index. The scatter of the modified damage index is significantly reduced compared to the original Park-Ang damage index. Then the finite element analysis models of 8 representative regular bridges samples were established with the main parameters variable such as the column height. The total 19120 increment dynamic analysis (IDA) curves were obtained by using the IDA method. These IDA curves are expressed in terms of one intensity measure (IM), i.e., the spectral acceleration at the fundamental period with 5% damping, and one engineering demand parameter (EDP), i.e., the modified Park-Ang damage index. At last, the probabilistic seismic demand model of regular bridges was established by using probability analysis based on the result of IDA curves. It is found that the seismic damage demand is reasonably standard beta distributed at given IM levels. The quadratic equation is suitable to establish the correlation between the mean value of the seismic damage demad and the IM. It is concluded that the established probabilistic seismic demand model is suitable for 3different site conditions and can largely simplify the computational effort of seismic demand in the performance-based seismic design and assessment of regular bridges.