Simulated Load-displacement Curves Research Articles

Relationship between the microstructural energy release rate of cortical bone and age under compression condition

Most studies evaluated the energy release rate of cortical bone macrostructure under Mode I, Mode II, and mixed Mode I-II loading conditions. However, testing the macrostructural energy release rate requires an initial crack and recording the applied load and the corresponding crack length in real-time, which may introduce measurement errors and differences with the actual fracture scenarios. To further understand how the energy release rate contributed to the cortical bone fracture characteristics, this study predicted the microstructural energy release rate of cortical bone and then investigated its age-related varitions. The microstructural energy release rate of femoral cortical bone in rats from different ages was back-calculated by fitting the experimental and simulated load–displacement curves under compression load. The trends in the microstructural energy release rate were revealed, and the underlying reasons for the age-related changes were investigated by integrating the discussion on the cortical bone mechanical parameters at various levels obtained from the previous experiment. The predicted microstructural energy release rate of femoral cortical bone in the rats from 1, 3, 5, 7, 9, 11, and 15 months of age were in the range of 0.08–0.12, 0.12–0.14, 0.15–0.19, 0.25–0.28, 0.23–0.25, 0.19–0.22, and 0.13–0.16 N/mm, respectively. The statistical analyses showed the significant differences in the microstructural energy release rate at different ages. The results indicated an increasing trend followed by a decrease from 1 to 15 months of age, and the correlations between microstructural energy release rate and age were significant. The age-related variations in the microstructural energy release rate may be linked to the changes in the microarchitecture, and the fracture load is influenced by the micro-level mechanical parameters. Notably, the age-related trends in microarchitecture and energy release rate were similar. These findings were valuable for understanding the mechanism underlying the weakening mechanical properties of cortical bone microstructure with age from an energy perspective.

Determination of the Gurson-Tvergaard-Needleman damage model parameters for simulating small punch tests of heat-resistant alloys

The small punch (SP) test is utilized to assess the mechanical characteristics and damage progression of heat-resistant alloys. The inverse finite element analysis method incorporating SP tests is a parameter identification method based on adjusting the accuracy of the simulated load-displacement curves. In this paper, the elastoplastic parameters of the Hollomon model and the damage parameters of the Gurson-Tvergaard-Needleman (GTN) model are determined based on the undamaged and damaged stages of the load-displacement curves, respectively. The whole stress-strain curves of the tested materials are then built using the results of finite element simulations of the tensile specimens of ZG15Cr2Mo1, P91, 316H, and Hastelloy X at room and elevated temperatures. Comparison with uniaxial tensile tests indicates that the simulated stress-strain curves closely resemble the experimental data from the tensile testing. In addition, the simulated damage evolution characteristics of the SP specimens are consistent with the mechanical model based on the actual deformation behavior. It is possible to comprehend the damage evolution process by analyzing the SP specimens’ stress and strain change characteristics.

Direct validation of 3D meso-scale fracture modelling of UHPFRC by in-situ micro X-ray CT wedge-split tests and parametric studies

3D meso-scale finite element models of ultra high performance fibre reinforced concrete (UHPFRC) based on in-situ micro X-ray Computed Tomography (CT) images are developed and validated in this study. The CT images at 16.9 μm voxel resolution from a progressive wedge-split test were converted into meso-scale 3D tetrahedron meshes. The short fibres, embedded in the mortar matrix, were modelled by truss elements with equivalent elastoplastic constitutive laws transformed from single fibre pullout load–displacement curves, so as to indirectly model the fibre–matrix interfaces. A concrete damage plasticity model was used to simulate damage and fracture in the mortar. The simulated load–displacement curves, final crack patterns, and load-crack opening curves were found in good agreement with the in-situ CT test results, and the non-vertical crack path was significantly affected by the overall orientation of fibres bridging the crack. Further simulations with all the fibres perpendicular to the tensile splitting direction showed that the peak load and fracture energy increased by 42 % and 45 % respectively from 1 % to 3 % fibre volume fraction. This indicates the need to optimize the fibre orientation for best mechanical performance according to the loading conditions.

Statistical modeling and reliability analysis of large-scale multi-tendon fiber-reinforced polymer cables

In this study, the classic fiber bundle model is exploited in the statistical modeling of fiber-reinforced polymer (FRP) cables. Important features of large-scale multi-tendon FRP cable are considered including initial random slack, uneven tensile deformation among tendons, and other statistical mechanical properties of tendon. Aiming at the prediction of load-displacement relation and design of thousand-meter-scale FRP cables, a parametric study and reliability analysis are conducted, in which the relation of reliability index β of cable and safety factor γ of FRP material is emphasized. In four different types of FRP cables from previous studies, the simulated load-displacement curves are in good agreement with experimental ones. The random slack and non-uniform deformation of tendons are found to have significant impacts on cable capacity. For a 10,000 m-long cable, compared to the original strength of the tendon, the retention rate of strength in real FRP cable can vary from 0.26 to 0.82, depending on the scattering of tendon strength. The recommended γ is 3.0, 3.2, and 3.4 for target reliability index βT = 3.7, 4.2, and 4.7, respectively. Then, the limits of design parameters for large-scale FRP cables are calculated under a given reliability index.

Seismic behaviors of CFT-column frame-four-corner bolted connected buckling-restrained steel plate shear walls using ALC/RAC panels

A Frame-Buckling Restrained Steel Plate Shear Walls (BRSPSWs) system has been designed, featuring a steel plate connected to frame elements, to withstand lateral loads like seismic or wind forces. This system incorporates recycled aggregate concrete (RAC) to create concrete-filled and concrete panels, promoting eco-friendly and sustainable construction materials. Two single-span, two-floor specimens were tested under cyclic quasi-static load. A four-corner bolted connection was used to connect the steel plate to the square concrete-filled steel tubes (CFTs) column and H-section beam, minimizing the potential deformation of the frame elements produced by the tension field of the steel plate after high-order bucking. The steel plate was sandwiched using either autoclaved lightweight concrete (ALC) or RAC panels. The study analyzed failure modes, load-displacement responses, and characteristic capacities. Test results inferred that BRSPSWs exhibited favorable cyclic behavior, with similar failure modes observed using both ALC and RAC panels. The buckling of steel plates was reduced, and the type of restrained panels had a negligible impact on buckling. Consequently, ALC panels can effectively replace RAC panels. Furthermore, bearing capacities and yield stiffness were primarily determined by the bolted connection forms. A finite element (FE) modeling was developed using ABAQUS software and validated against test results. This FE modeling method successfully simulated failure modes and load-displacement curves. Parametric analyses were conducted and revealed that bearing capacity and yield stiffness positively correlated with steel plate thickness, bolt diameter, and the number of bolts but negatively correlated with the axial compression ratio. In contrast, the panel thickness and span length had a minor impact due to shear deformation in the bolted connection. Based on the test results and parametric studies, an equation for the yield-bearing capacity of BRSPSWs was proposed and verified.

Study on constitutive relationship of 6061 aluminum alloy based on Johnson-Cook model

Uniaxial tensile tests are conducted on 6061 aluminum alloy sheets at different strain rates of a certain temperature and different temperatures of a certain strain rate. The true stress-strain curves show that the flow stresses are negatively correlated with strain rates and temperatures. Based on the Johnson Cook (J-C) constitutive model, the modified J-C model is constructed by replacing the strain term with a Voce hardening model and correcting the strain rate sensitivity coefficient and the thermal softening exponent. Compared with the J-C model, the modified J-C model has a smaller average absolute error and more accurately describes the plastic stress-strain relationship of 6061 aluminum alloy under various deformation conditions. Furthermore, the modified J-C model is also used for numerical simulation of uniaxial tension. The good agreement between the experimental and simulated load-displacement curves further verifies the usefulness of the modified J-C model. Finally, the microscopic mechanism by which deformation speeds affect ductility is analyzed by scanning electron microscopy (SEM).

A surrogate model based calibration method for structural adhesive joint progressive failure simulations

ABSTRACT An integrated adhesive material model calibration method is proposed for adhesively bonded joints’ deformation and progressive failure simulations under mixed loading modes. In this method, a surrogate model is trained to express the intrinsic numerical relationship between the key parameters (e.g., the yield normal stress and yield shear stress) and the simulated load-displacement curves of the bonded specimens. The parameter calibration process of the material model under multiple loading conditions is described as a multi-objective optimization problem. To minimize the load-displacement curve errors among the CAE simulation model and the experiment data, the model parameters are calibrated effectively based on the surrogate model using the genetic algorithm. The validity and efficiency of the proposed calibration method is verified by comparing the test data under various loading conditions. The better precision and efficiency indicates the potential of using this framework to effectively calibrate material properties without performing time-consuming CAE simulations.

Numerical analysis of compressive deformation for random closed-cell Al foam model

Most cellular solids presented random structure, while practically periodic models were often used in structure-property relations and numerical models. The finite element method was used to create a 2D random model that replicated the deformation characteristics of cellular models. The influences of porosity and strain rate on the deformation characteristic, energy dissipation mechanisms were investigated. The Poisson’s ratio evolution during compression was also studied. The simulated load-displacement curves were found to be consistent with experimental results, both containing elastic stage, plateau stage, hardening stage and densification stage. The yield load and plateau load were insensitive to the strain rate. In addition, it was also found that the generation and propagation of multiple random shear bands were responsible for the load-displacement characteristic. At the cell/membrane level, four failure modes and corresponding energy dissipation mechanisms were revealed. Moreover, the Poisson’s ratio decreased first and then increased with strain, which right manifested the compressibility of 2D foam in the initial stage and the densification in the end of compression. Meanwhile, the change of the Poisson’s ratio with porosity didn’t follow monotone function relation.

Experimental Investigation on the Mechanical Performance of Steel-ECC Composite Girders with Corrugated Webs under Negative Moment.

In order to improve the cracking performance in the negative moment region of composite continuous girder bridges with corrugated webs, engineered cementitious composite (ECC) is used instead of conventional normal concrete (NC). Web and concrete types are used as the main research parameters in experiments. The test results indicate that steel-ECC specimens have a higher flexural load capacity and stiffness than steel-NC specimens. The cracks of steel-ECC specimens are characterised by small width and dense distribution. Nonlinear finite element models are established and verified by experimental results. The simulated load–displacement curves are similar to the experimental ones, and the models have a high degree of accuracy. The ECC slab strength, thickness and width are used as parameters for the investigation to analyse the effect of the ECC slab on the flexural bearing capacity of composite girders. Compared with the results of calculations according to the code, the bearing capacity obtained from the parametric analysis is higher. It suggests that the contribution of the ECC slab needs to be considered when calculating the bearing capacity of the steel-ECC composite girder with corrugated webs.

Finite element analysis of the shear capacity of stainless-steel screw connections

Stainless-steel has been widely applied in engineering for its good corrosion resistance and low life-cycle cost. The use of screws in the thin sheet has the advantages of simple construction and tight connection, so it is widely used in open-air maintenance systems. However, the mechanical performance of stainless-steel screw connections is quite different from that of carbon steel due to the material difference, which needs further research. In this paper, finite element method was carried out to simulate the shear performance of the stainless-steel screw connections. The simulated failure modes were consistent with the experimental results, the simulated load–displacement curves were close to the experimental results, and the difference was within 10%. A variety of parametric studies utilizing the finite element method (FEM) had been performed on the shear capacity of stainless-steel screw connections, which included sheet thickness, spacing and connecting length. Results shown that the connecting length was the main factor affecting the shear capacity of the stainless-steel screw connections. For equal-thickness connection (t1 = t2 = 1.5 mm, 2.0 mm, 3.0 mm), when the connecting length was within 6d-60d, the shear capacity increased linearly with the increase of the connecting length. For unequal-thickness connection (t1 = 1.5 mm, t2 = 2.0 mm/t1 = 2.0 mm, t2 = 3.0 mm/t1 = 2.0 mm, t2 = 5.0 mm), when the connecting length was within 6d-45d, the shear capacity increased linearly with the increase of the connecting length. However, when the connecting length was within 45d-60d, the end screw occurred shear failure first, its shear capacity almost no longer increased. The change of screw spacing and the sheet thickness had few effect on the shear capacity. Based on reliability research, the resistance factor and design strength were proposed. For shear failure,γR=1.273, fvb=275MPa, and for bearing failure, γR=1.306, fvb=315MPa.

Flexural property evaluation of web reinforced GFRP-PET foam sandwich panel: Experimental study and numerical simulation

This work focus on the flexural property of polyethylene terephthalate (PET) foam-filled lattice composite sandwich panels subjected to four-point bending (FPB). The effects of different face sheet and core thicknesses on the flexural properties of the sandwich panels were analyzed. Experimental results indicated that the glass fiber-reinforced polymer (GFRP) webs can effectively prevent the sandwiches from catastrophic failure , the failure modes of the structures are dominated by foam shear, top face sheet compressive, and top face sheet-core debonding. Increasing the face sheet and PET foam thickness can effectively improve the ultimate load of the panels by 88.9% and 115.6%, respectively. An analytical model was employed to accurately predict the bending stiffness , ultimate load, and failure modes of the structures. The errors between theoretical predicted and experimental results are within 10% in terms of bending stiffness and ultimate load. Furthermore, a 3D numerical model was built to understand the failure modes and responses of the structures, a continuum damage material model for PET foam was imported into ABAQUS software by VUMAT subroutine, and Hashin failure criterion was used for GFRP. The simulated failure modes and load-displacement curves were in good agreement with experimental results.

A Numerical Method for Applying Cohesive Stress on Fracture Process Zone in Concrete Using Nonlinear Spring Element.

Aiming at the numerical simulation of the entire crack propagation process in concrete, a numerical method is proposed, in which cohesive stress on the fracture process zone (FPZ) is simulated and applied by a nonlinear spring element. Using displacement control, the cohesive stress values on the FPZ are obtained from solving a system of nonlinear equations through an iterative process. According to a crack propagation criterion based on initial fracture toughness, the approach adds the spring elements to finite element analysis when simulating mode I crack propagation in standard three-point bending notched concrete beams with different strengths, initial crack ratios , and depths (D). The simulated load versus displacement (P-Delta) curves are performed to recalculate the fracture energy and verify the accuracy of cohesion in the proposed method. The simulated load versus crack mouth opening displacement (P-CMOD) curves are consistent with the previous experimental results. Subsequently, the variations of the FPZ length and the crack extension resistance ( curves are studied according to the proposed iterative approach. Compared with the existing methods using a noniterative process, the iterative approach generates a larger maximum FPZ length and curve where the FPZ length is mainly determined by the fracture energy, tensile strength, and geometry shape of the beam, and the curve is primarily determined by the fracture energy and FPZ length. The significant differences in numerical results indicate that the applying cohesion is essential in numerical simulation. It is reasonable to conclude that the proposed nonlinear spring element is more applicable and practical in the numerical simulation of the concrete mode I crack propagation process by improving the accuracy of the cohesion applied on the FPZ.

Experimental and numerical investigation on the seismic performance of concrete-filled UHPC tubular columns

This paper presents an experimental and numerical investigation on a novel composite column, i.e., concrete-filled ultra-high performance concrete (UHPC) tubular (CFUT) column. One control RC column and three CFUT columns with different column parameters were tested under combined constant axial compression and lateral cyclic loading to investigate the influence on the seismic performance. The test results indicated that the good synergy work performance of the UHPC jackets and the core concrete allowed a continuous contribution of the UHPC jackets to the load-bearing capacities. Compared with the RC column, the CFUT column had a good seismic performance with significant enhancements in the initial lateral stiffness and lateral load-bearing capacity. With the wide-spread multi-cracking behavior due to the steel fiber bridging effect, the CFUT columns also exhibited improved deformation capacity together with decreased residual drift ratios. Besides, a finite element (FE) model was also developed to simulate the response of the composite columns. The experimental and simulated load-displacement curves agreed well, and the load versus deformation behavior of the composite columns could be properly captured.

Bearing Capacity of Hollow GFRP Pipe-Concrete-High Strength Steel Tube Composite Long Columns Under Eccentrical Compression Load

To investigate the bearing capacity of the hollow Glass Fiber Reinforced Polymer (GFRP) pipe-concrete-steel tube composite long columns subjected to eccentrical compression load, 33 hollow GFRP pipe-concrete-steel tube composite long columns have been designed. The slenderness ratio (λ), compressive strength of concrete cube (fcu), eccentricity (e) and so on are the main parameters. Based on constitutive models for steel, GFRP and confined concrete, numerical simulation of the hollow GFRP pipe-concrete-high strength steel tube composite long columns has been carried out by using software ABAQUS. The rationality of the constitutive models and modeling method has been verified by comparing the experimental and simulated load-displacement curves. The influence of different parameters on the mechanical behavior of this kind of column has been investigated. Results show that with the increasing of t1, t2 and fcu, the ultimate eccentrical compression bearing capacity of the specimen increases. With the increasing of e, the ultimate displacement of the specimens increases, while the ultimate eccentrical compression bearing capacity decreases. The eccentricity has a significant influence on the ultimate eccentrical compression bearing capacity. With the increasing of λ, the ultimate eccentrical compression bearing capacity of the specimens gradually decreases. The specimens suffer from ductile failure. The formula of the ultimate eccentrical compression bearing capacity of the composite columns is obtained by statistical regression. The study can provide theoretical support for the application of the composite columns in practical engineering.

Ex-situ micro X-ray computed tomography tests and image-based simulation of UHPFRC beams under bending

Micro-structures of fibre reinforced composites play a pivotal role in their damage, fracture and failure mechanisms. This study first carried out ex-situ micro X-ray Computed Tomography (μXCT) tests of three small ultra-high-performance fibre reinforced concrete (UHPFRC) beams under progressive three-point bending. The first two beams were continuously loaded until failure and their central regions with the main flexural crack were scanned by μXCT before and after the test. The third beam was subjected to five cycles of loading-unloading until failure, and was scanned by μXCT after each unloading. The 3D μXCT images with 30 μm voxel resolution were then processed and analysed, and the spatial distribution, number, orientation and dimension of pores and fibres were statistically quantified. The micro-scale failure mechanisms, such as fibre bridging of cracks, fibre-matrix interfacial slipping and debonding, and matrix failure, were visualised and analysed. The μXCT images of the first two beams were then segmented and directly converted to meso-scale finite element models based on orientation-dependent bond-slip relations for the fibre-matrix interfaces and continuum damage plasticity for the matrix. The simulated load-displacement curves, fracture processes and final crack morphologies were found in excellent agreement with the tests. It was also found that the position, dimension and orientation of fibres and pores have significant effects on the damage and fracture initiation and evolution from both the tests and the simulations.

Experimental and simulation analysis of residual topography dominated deformation mechanism of nanoindentation: a case study of Inconel 625 superalloy

The microscopic deformation behavior of Inconel 625 superalloy has been investigated by means of nanoindentation experiments and crystal plasticity finite element simulations. Based on the electron backscattered diffraction characterizations, the nanoindentation simulations were performed on grains with various orientations. The simulated load–displacement curves match well with those of experiment and the maximum difference in materials hardness between the experimental and the simulation result is about 6.86%, which is within the accuracy of the model. Moreover, surface Schmid factor (SSF) and interior Schmid factor (ISF) were proposed out and the scanning electron microscope and atomic force microscope characterizations were carried out. The results show that the pile-up tends to occur at the locations with a large SSF. Subsequently, the simulations of nanoindentation on [001]-, [011]-, and [111]-oriented grains were performed by the established model. It is revealed that the residual topography changes periodically when the indenter is fixed and the crystal only rotates around the Z-axis of the sample coordinate system. Combining with the analysis of the ISF, this periodicity of residual topography reflects the superimposed effect of the slip systems, and a large ISF promotes the in-plane displacement of the interior material which inhibiting the evolution of pile-up, while a small ISF leads to a high pile-up.

Modelling and estimation of critical fracture energy, Gfr in ductile to brittle transition zone for characterising crack growth phenomenon in 20MnMoNi55 RPV steel

One of the methods for describing the phenomenon of stable crack growth in ductile materials is the estimation of critical fracture energy, Gfr as proposed by Marie and Chapuliot. These methods of calculation of Gfr are applicable for large crack growth. However, the method for estimating Gfr was re-investigated for short crack growth. It was observed in the previous works that the Gfr values obtained for short crack growth gradually increases and saturates to the value at large crack growth. This saturated Gfr value can be claimed to be a material property. It was also shown that a correction factor (function of critical CTOD and crack growth) when introduced to this saturated value of Gfr helps in obtaining the unsaturated values of Gfr. In the present work, an attempt is made to estimate Gfr using the above mentioned re-investigated idea at the upper part of ductile to brittle transition temperature regime (0 °C to-60 °C). At sub-zero temperatures stable crack growth is much less when compared to the room temperature. The correction factor which is a function of saturated Gfr value, CTOD and crack growth is found to be suitable for the CT specimen results even at low temperature. The values of unsaturated Gfr values thus obtained using the correction factor are then used to simulate load versus load line displacement curves. The simulated load versus load line displacement curves at different temperatures are in good agreement with the experimental results irrespective of change in a/W ratios of the CT specimen.

Determination of the tensile and fracture properties of ductile materials by small punch testing

ABSTRACT The uniaxial tensile and fracture properties are the basic data for the structural integrity assessment of ductile material. In this study, the stress-strain relations of ductile materials are predicted by the SPT-related stress-strain relation (SPT-SR) model directly through SPT experiment, which agree with the relations determined by the finite-element-analysis aided testing (FAT) method. Further, the experimental procedures of SPT are simulated by combining the Gurson-Tvergaard-Needleman (GTN) model and the predicted stress-strain relations. The parameters of GTN model can be determined when the simulated load-displacement curves of SPT specimens coincide with the experimental results. Finally, the ductile crack propagation behaviors of the single edge-notched bending (SEB) specimens are simulated utilizing the calibrated GTN model, and the corresponding J resistance curves are successfully predicted via the normalization method.

An application of FEM in the determination of tensile properties for work-hardened carbon steel by means of small punch test

The determination of tensile properties from a small punch (SP) test by using a finite element method (FEM) has been studied. First, a finite element (FE) simulation of the SP test using true stress-strain curves including post-necking strain data of work-hardened SM490A carbon steel specimens was conducted. The simulation was validated with actual experimental results, which showed that the FE model can effectively reproduce the load-displacement curves without using a damage modeling technique. The FE model was then used to investigate an empirical correlation between the punch loads and the material parameters, including yield strength and ultimate tensile strength. The results indicated that the empirical constants are dependent on specimen thickness and may be valid for only a limited range of test configurations and materials. To expand the applicability of the SP test in the assessment of tensile properties, an inverse finite element method (iFEM) consisting of the iterative finite element calculation, bisection method, and Ludwik’s constitutive model was developed. Through the procedure, true stress-strain curves were constructed from the simulated load-displacement curves of hypothetical materials based on the SM490A steel specimens. Finally, yield strengths and ultimate tensile strengths of the carbon steel specimens were determined and found to be within 5.2% and 2.8% discrepancies, respectively, from the uniaxial tensile test results. iFEM provides consistent estimations of tensile properties with almost no influence of specimen thickness.

Damage propagation and strength prediction of a single-lap interference-fit laminate structure

Experimental and finite element research was conducted on the bolted interference fit of a single-lap laminated structure to reveal the damage propagation mechanism and strength change law. A typical single-lap statically loading experiment was performed, and a finite element damage prediction model was built based on intralaminar progress damage theory. The model was programmed with a user subroutine and an interlaminar cohesive zone method. The deformation and damage propagation of the specimen were analyzed, and the failure mechanism of intralaminar and interlaminar damage during loading was discussed. The effect of secondary bending moment on load translation and damage distribution was revealed. The experimental and simulated load-displacement curves were compared to validate the developed model’s reliability, and the ultimate bearing strengths under different fit percentages were predicted. An optimal percentage was also recommended.