Experimental Load Curves Research Articles

Phase Field Coupled Finite Deformation Plasticity Formulation of Ductile Fracture With Nonlinear Kinematic Hardening and Modified Energy Release Function

ABSTRACTA ductile damage theory is presented by coupling the covariant formulation of finite deformation plasticity with the phase field modeling of fracture, including kinematic hardening for the ductile response of the materials. A phase field coupled nonlinear kinematic hardening equation is proposed in the reference configuration having equivalent representation through the Lie derivative of the kinematic hardening tensor by push‐forward operation in the spatial configuration, thus ensuring the satisfaction of frame invariance. To capture the correct physical response of the material by the phase field evolution equation, the fracture driving function, that is, the difference between the sum of elastic and plastic energies and threshold energy, after the damage initiation is modified by an energy release controlling function, which is an empirical relation of equivalent plastic strain. In defining the energy release controlling function, well‐defined points with physical significance in the experimental load versus displacement curve are used. To simulate the response of the material in relatively large time steps, a modified staggered scheme is presented, evaluating the fracture driving and energy release controlling functions from the previous converged step and using the updated phase field variable in the weak form of the momentum balance equation. To quantify different material parameters from available experimental results in the literature, the developed phase field coupled elasto‐plastic model uses a neural network optimization procedure consisting of neural network training together with optimization in MATLAB and finite element model evaluation in Abaqus user element subroutine UEL. Model capabilities are demonstrated by simulating the crack propagation in complex 3D geometries such as the second and third Sandia Fracture Challenges.

The Effect of Jacket Area on The Behaviour of Repaired/Strengthened Reinforced Concrete Columns

acketing is the most popular method for strengthening reinforced concrete columns under axial loading. This repair and strengthening technique is widely used not only in Türkiye but also in other technologically developed countries. In this study, the effectiveness of this method is investigated by experimentally testing two parameters: column section geometry and jacket thickness. The specimens were enlarged on all four sides to understand how the thickness of the jacket layer affects the behavior of the column. Using the experimental data, load versus deformation curves were plotted for each specimen. The parameters (strength, rigidity, ductility, and energy dissipation capacity) that determine the behaviour of the reinforced column were then analysed. At the end of this study, the effects of column section geometry and jacket thickness on the jacketing method are discussed, providing valuable preliminary data for future experimental studies.

Application of high performance concrete for reconstruction

One of the sustainability aspects of the construction is a sufficient durability. In objectively justified cases, the durability is enhanced by reconstruction. To ensure economic design of the reconstruction, non-liner approaches are often applied. This paper deals with aănonlinear numerical simulation of disassembled reinforced concrete (RC) panels strengthened by an ultra-high performance concrete (UHPC) layer. Based on the prior experimental programme, simulations of four-point bending tests of the original and strengthened panels are created using software ATENA Science. Calibration of the material parameters is based on the destructive and non-destructive investigations performed in the experimental programme. The comparison of the experimental and numerical model loading curves indicates that additional mechanical testing will be needed in order to achieve an accurate numerical simulation. Although the bending test of the RC panel and the crack mouth opening displacement (CMOD) test performed on the applied UHPC beam were calibrated, the final model of the UHPC strengthened panel does not correspond completely with the experimental measurements. In this paper the possible reasons for this result are discussed.

The Non-Equivalence of Pyramids and Their Pseudo-Cones: Important New Insights

The simulation of indentations with so called “equivalent” pseudo-cones for decreasing computer time is challenged. The mimicry of pseudo-cones having equal basal surface and depth with pyramidal indenters is excluded by basic arithmetic and trigonometric calculations. The commonly accepted angles of so called “equivalent” pseudo-cones must not also claim equal depth. Such bias (answers put into the questions to be solved) in the historical values of the generally used half-opening angles of pseudo-cones is revealed. It falsifies all simulations or conclusions on that basis. The enormous errors in the resulting hardness HISO and elastic modulus Er-ISO values are disastrous not only for the artificial intelligence. The straightforward deduction for possibly ψ-cones (ψ for pseudo) without biased depths’ errors for equal basal surface and equal volume is reported. These ψ-cones would of course penetrate much more deeply than the three-sided Berkovich and cube corner pyramids (r a/2), and their half-opening angles would be smaller than those of the respective pyramids (reverse with r > a/2 for four-sided Vickers). Also the unlike forces’ direction angles are reported for the more sideward and the resulting downward directions. They are reflected by the diameter of the parallelograms with length and off-angle from the vertical axis. Experimental loading curves before and after the phase-transition onsets are indispensable. Mimicry of ψ-cones and pyramids is also quantitatively excluded. All simulations on their bases would also be dangerously invalid for industrial and solid pharmaceutical materials.

Research and Modeling of Viscoelastic Behavior of Elastomeric Nanocomposites

The paper presents results of studying mechanical properties of polymer composites depending on types of filler particles (granular - carbon black, nanodiamonds; layered - graphene plates; fibrous - single-walled nanotubes). These nanofillers differ greatly from each other in their structure and geometry. A significant difference in behavior of nanocomposites was revealed even with little introduction of particles into the elastomer. The highest level of reinforcement of the matrix was obtained when single-wall nanotubes and detonation nanodiamonds were used as fillers. The viscoelastic properties and the Mullins softening effect [1-4] were investigated in experiments performed with material samples subjected to complex uniaxial cyclic deformation. In these experiments, the amplitude of deformations was changed step by step; and at each step a time delay was specified to complete rearrangement processes of the material structure. It was found that a pronounced softening effect after the first cycle of deformation and significant hysteresis losses occur in the material filled with single-walled nanotubes. These characteristics are insignificant for the rest of nanocomposites until elongation increases twofold. In accordance with the obtained results, a new version of the mathematical model to describe properties of the viscoelastic polymer materials was proposed. The constants of the constitutive relations were calculated for each material; the theoretical and experimental load curves were compared. As a result, the introduced model is able to describe the behavior of elastomeric nanocomposites with a high accuracy. Moreover, this model is relatively easy to use, suitable for a wide range of strain rates and stretch ratios and does not require the entire history of deformation as needed for integral models of viscoelasticity.

Experimental analysis and numerical optimization of a thermoplastic composite in crashworthiness

In this work, we present an experimental analysis and a numerical optimization study for the material parameter identification of an impact attenuator made of a brand new All-PP thermoplastic composite material subjected to an axial impact load. After an experimental characterization of the material, a Finite Element (FE) numerical model of the impact attenuator is created and simulated using the LS-DYNA explicit software. Subsequently, in order to capture the force-displacement trend of the crush experimental test, a fine-tuning of some relevant material parameters through surrogate-based optimization techniques is performed. The optimization process mainly consists of (1) defining a set of target points on the load-displacement curve where to evaluate the Mean Squared Error (MSE) between the numerical and the experimental values; (2) using a Design of Experiments technique to provide a sample set on which expensive deterministic simulations are performed; (3) constructing as many surrogate approximations as the number of target points in order to predict how the load values change over the parameters’ domain; (4) predicting an overall MSE surface that is optimized by means of a genetic algorithm in a sequential domain reduction iterative procedure. Results show a good agreement between the numerical and the experimental impact load and energy curves, and hence confirm that surrogate-based optimization is a valuable technique to refine the material parameters in the numerical simulation of composite structures.

Finite Element Analysis of Adhesive Failure of Solid Composite Propellant Multi-material Structure for Underwater Intelligent Equipment

This paper is a consecutive work based on the last paper “Finite element analysis of viscoelastic/damage behaviors of composite solid propellant for underwater intelligent equipment”. This paper studies adhesive failure behaviors of multi-material structure in underwater intelligent equipment, which includes the propellant layer/lining layer/adiabatic layer/aluminum layer. First, the hyperelastic mechanical properties for ethylene–propylene–diene monomer for adiabatic layer are predicted by using the Mooney–Rivlin constitutive model, where the material parameters are fitted by combining with theoretical and experimental load curves. Second, the adhesive failure between the propellant layer and the lining layer is predicted for the designed multiple material layers under shear loads by combining with the bilinear cohesive model, the constitutive models for the propellant and adiabatic layer materials. Finally, the adhesive failure mechanisms and the load responses are studied for the shear specimens.

Compressive transverse fracture behaviour of pultruded GFRP materials: Experimental study and numerical calibration

This paper presents a study on the transverse fracture behaviour of pultruded glass fibre reinforced polymer (GFRP) materials in compression, namely the assessment of transverse compressive fracture toughness (G2−) and transverse compressive residual strength (σr). These properties were assessed through experimental Compact Compression (CC) tests of six different GFRP materials, which were coupled with a data reduction method to determine experimental predictions of G2− and numerically calibrated as a function of the experimental load vs. displacement curves. Through this process, the expected experimental overestimation of G2−, attributed to contact stresses behind the notch tip, was evaluated and accurate numerical estimates of G2− were determined. The numerical calibration considered both G2− and σr, by considering a bi-linear cohesive law. Through the numerical calibration, the G2− results ranged between 36 and 67 N/mm and σr values varied from 9% to 16% of transverse compressive strength (7.6 and 16.9 MPa, in absolute values). Finally, the G2− results were analysed as a function of transverse fibre reinforcement percentage and compared to transverse tensile fracture toughness results (G2+) determined in a previous work. This study showed that G2− is generally higher than G2+ and that the compressive-to-tensile ratio is inversely proportional to the transverse reinforcement percentage.

Modeling material behavior during continuous bending under tension for inferring the post-necking strain hardening response of ductile sheet metals: Application to DP 780 steel

Continuous bending under tension (CBT) testing can stretch ductile sheet metals significantly more than simple tension (ST) testing. Strength and plastic strain levels increase with the number of CBT cycles and substantially exceed those achieved in ST. Taking advantages of the improved elongation-to-fracture (ETF) achieved by CBT, samples of DP 780 steel are pre-deformed to several strain levels by interrupting their CBT testing. Sub-size specimens are machined from the CBT interrupted specimens and tested in ST. The flow curves from these secondary ST tests are then shifted according to the axial strain accumulated during pre-deformation by CBT to determine a large strain (post-necking) flow curve of the material. The identified large strain flow curve is validated with two approaches. First, the large strain flow curve is used to simulate the load versus displacement curve during CBT to large number of CBT cycles. Second, the curve is used to simulate the flow curves based on the secondary ST testing. The simulations are performed using isotropic hardening (IH) and combined isotropic-kinematic hardening (CIKH) material models. The latter model is calibrated using a set of large strain cyclic tension-compression data. An automated procedure is developed for the creation of sub-size specimens from the finite element (FE) mesh of the interrupted CBT specimen to facilitate efficient secondary ST simulations. The procedure involves cutting of the FE mesh into the sub-size specimen shape by Boolean operations in Abaqus software followed by generation of volume FE mesh and mapping of the state variables. The state variables are mapped to simulate deflection of the specimens, as the residual stress field from the prior CBT simulation evolves to reach a new equilibrium. It is found that the model reproduces the experimental load versus displacement curve, including the succession of spikes and plateaus typical of CBT, very closely. The model also predicts yielding of the interrupted sub-size specimens further verifying the identified curve. The predictions demonstrate the utility of the developed methodology for inferring the post-necking strain hardening behavior of sheets.

Experimental study on ultimate strength of steel-welded ring-stiffened conical shell under external hydrostatic pressure

This paper reports experimental and numerical investigations on the ultimate strength responses of steel-welded, ring-stiffened conical shells when subjected to external hydrostatic pressure. Four small-scale shell models were fabricated from general structural steel by cold bending and arc welding. First, hydrostatic pressure tests were performed to investigate the collapse behaviour of the models. The influences of different parameters were also studied experimentally. Before the experiments, quasi-static tensile tests were performed to obtain detailed characterisation of the test model material. In addition, the initial imperfection of the shell and other as-built geometry parameters were carefully measured. The test was conducted using compressed water in a small-sized chamber and loaded to collapse. Three models with heavy stiffeners were failed by local buckling at the shell between the ring frames. Another model failed by the overall buckling of the adjacent frames together with the shell. The numerical computations were performed on the finite element code of ABAQUS FEA. The imperfection due to fabrication, such as initial out-of-circularity, and residual stresses due to welding are simulated. The quasi-static response was compared with the experimental load and plastic deformation curves. The numerical results revealed a close agreement between the collapse pressure prediction and failure modes of the simulation and the experiment.

Experimental Investigation of Damage Formation in Planar Fibrous Networks During Stretching

This paper presents the results of unidirectional strain-controlled experiments on fibrous electrospun networks used to study damage formation during elongation. The experimental loading curve shows a symmetrical parabolic type dependence at large scale and saw tooth-like force−extension behaviour at small scale. The damage formation was quantified by determining the number and the magnitude of abrupt force drops. The experiments evidenced that damage evolution is a consequence of strain induced random events. The frequency distribution of the number of damages as well as the magnitude of rupture force were represented by histograms. The results of the present study provide a better insight into damage tolerance and complex nonlinear tensile properties of electrospun networks. In addition, it could suggest a possible probabilistic approach to the fiber bundle model which has mainly motivated this study.

The influence of fractal dimension in the microcontact of three-dimensional elastic-plastic fractal surfaces

Microcontact affects the fabrication and assembly of MEMS/NEMS system, the contact between thin film microcavity and microcantilever beam, and the motion of microstructure. In this work, in the microcontact of three-dimensional elastic-plastic Weierstrass-Mandelbrot (W-M) fractal surfaces, influence of fractal dimension was studied based on a comprehensive contact model. With increasing fractal dimension, maximum microcontact force in the plastic deformation zone shows parabolic change; comparably, the intermediate force in elastic zone parabolically varies. For both the forces, the minimum values are obtained when the fractal dimension is 2.5. Besides, in the plastic deformation zone, the real contact areas increase with the fractal dimension. Experiments were completed to compare with the numerical analysis. The results show that the simulated contact force curve is in line with the experimental load curve when Young’s modulus E and hardness H are equal to the actual measured values. Nevertheless, it will greatly deviate from the experimental load curve when E and H differ from the measured values.

Implementation and calibration of meso-scale modeling technique for simulation of tensile behavior of fabric materials

Abstract Present paper investigates the simulation of quasi-static response of fabric materials subjected to uniaxial tensile loading. The purpose of this research is to simulate the fabrics mechanical behavior accurately determining the quasi-static elastic and failure properties of fabric yarn and to rank, from the analysis point of view, the parameters which influence the fabric behavior. In particular, a meso-scale approach was employed to model the behavior of different para-aramid fabrics using LS-DYNA software whereas the Nelder & Mead Simplex optimization algorithm was implemented for the determination of material model's parameters by the fitting of numerical and experimental tensile loading curve.

Toward an understanding of the effect of surface roughness on instrumented indentation results

Performing indentation tests on rough surfaces at the microscale creates non-negligible scatter of the load–indentation depth curves and leads to an inaccurate computation of mechanical properties. In previous work, the minimization of the error between the shapes of the experimental loading curve and the shapes predicted by Bernhardt’s law enabled the macrohardness of the material to be determined with accuracy and to identify a relationship between the standard deviation of the errors of shapes and the root-mean-square roughness (Sq) computed at the scale of the indentation imprint. In this paper, a semi-analytical model applied to roughness measurements is used to understand this relationship. Good agreement is found between the model results and the experimental results. Analysis of the semi-analytical model confirmed that the identified relationship is caused by the topography and not by some experimental bias and that the relevant scale for the computation of Sq is the scale of the indentation imprints (15 µm). However, the relationships found with the model and the experimental results show different slopes and y-intercepts. The y-intercept found with the numerical curves is negligible compared with the y-intercept identified with the experimental curve, which is equal to 30 nm. This indicates that even if Sq is equal to zero, the zero-point of the curve is not accurately determined by the instrumented indentation device. As for the differences in slope, these may be partly due to experimental noise and the differences of methodology of detections of first-contact for the recording of the load–displacement curves. Overestimation of the resistance of abrasion debris by the semi-analytical model may also explain the differences of slopes. However, further testing is required to confirm this hypothesis.

Direct powder forging of PM nickel-based superalloy: densification and recrystallisation

Powder metallurgy nickel-based superalloys have been widely used in high temperature applications. For these materials, a fully dense and fine-grained microstructure is important. Full densification can be achieved by a suitable processing technique, while the latter can be achieved through recrystallisation for which valuable guidance is provided by the information about recrystallisation nuclei. In this study, a fully dense powder metallurgy nickel-based superalloy component has been produced by a new manufacturing method—direct powder forging—using a single acting hydraulic press under normal atmosphere. Boundary misorientation of the produced material has been analysed to determine the degree of recrystallisation nucleation. A finite element model for direct powder forging has been developed in DEFORM-2D/3D and validated by comparing experimental and simulated load curves. The relationship of stress and strain state with densification and recrystallisation nucleation degree has been analysed. It was found that the direct powder forged FGH96 alloy has a much higher recystallisation nucleation degree and more recrystallised sub-grains, compared with those of the hot isostatic pressed material. Within the forged component, a higher recystallisation nucleation degree resides in the material near the container wall where greater values of shear strain rate have operated.

Application of a tangent curve mathematical model for analysis of the mechanical behaviour of sunflower bulk seeds

AbstractThis paper evaluate the use of a tangent curve mathematical model for representation of the mechanical behaviour of sunflower bulk seeds. Compression machine (Tempos Model 50, Czech Republic) and pressing vessel diameter 60 mm were used for the loading experiment. Varying forces between 50 and 130 kN and speeds ranging from 10, 50, and 100 mm min-1were applied respectively on the bulk seeds with moisture content 12.37±0.38% w.b. The relationship between force and deformation curves of bulk seeds of pressing height 80 mm was described. The oil point strain was also determined from the different deformation values namely 30, 35, 40, and 45 mm at speed 10 mm min-1. Based on the results obtained, model coefficients were determined for fitting the experimental load and deformation curves. The validity of these coefficients were dependent on the bulk seeds of pressing height, vessel diameter, maximum force 110 kN, and speed 10 mm min-1, where optimal oil yield was observed. The oil point was detected at 45 mm deformation giving the strain value of 0.56 with the corresponding force 16.65±3.51 kN and energy 1.06±0.18 MJ m-3. At the force of 130 kN, a serration effect on the curves was indicated; hence, the compression process was ceased.

Natural fiber composite: Challenges simulating inelastic response in strain-controlled tensile tests

Problems occurring, when nonlinear time-dependent material model with parameters identified in creep tests is applied to simulate high-strain response in strain-controlled tests, are described and analyzed. Reasons for discrepancies with experimental loading curves are revealed. Presented numerical/experimental examples deal with three bio-based composites showing highly nonlinear behavior due to damage, nonlinear viscoelasticity and viscoplasticity. Schapery's approach for viscoelasticity and Zapas' model for viscoplasticity are used. The model is generalized to include microdamage effect. It is shown that the main problem in simulations at high stresses is the reliability of data from creep test for model identification in this region because creep rupture limits the available data region and extrapolation to higher stresses is rather uncertain. Alternative solution is to employ relaxation tests at high strains to obtain the missing information. However, it would work only in absence of viscoplastic strains: viscoelastic relaxation functions cannot be determined by maintaining constant total strain if viscoplastic-strain is developing. Based on sensitivity analysis of composite response to variations of the elastic modulus, damage, viscoelastic and viscoplastic parameters, suggestions are made for improving (further “tuning”) the model in high stress region by using tensile stress–strain curves in quasi-static loading.

Predictions of frame compliance and apex morphology in sharp nanoindentations

If all components in a nanoindentation system are well calibrated and a reference material has unique hardness, H and reduced modulus, Er independent of the indentation depths, the load, L and the penetration depth, h in the indentation loading curve of the reference material can be correlated by L=Kh2. Here the constant K is expressed by H, Er and indenter geometry constants. By using H and Er of a fused silica and the Berkovich geometry, an analytical expression for the indentation loading curve could be derived. To compare with this analytical loading curve, experimental indentation data were measured with two commercial nanoindenters. The experimental loading curves shifted leftward or rightward from the analytical loading curve and this depth deviation was attributed to improper calibration of the nanoindenters. Quantitative calibrations of frame compliance and indenter bluntness were tried for the raw nanoindentation data and this resulted in consistent nanoindentation data regardless of the used nanoindenters.

Plastic characterization of metals by combining nanoindentation test and finite element simulation

Materials with the same elastic modulus E and representative stress and strain (σr, ɛr) present similar indentation–loading curves, whatever the value of strain hardening exponent n. Based on this definition, a good approach was proposed to extract the plastic properties or constitutive equations of metals from nanoindentation test combining finite element simulation. Firstly, without consideration of strain hardening, the representative stress was determined by varying assumed representative stress over a wide range until a good agreement was reached between the computed and experimental loading curves. Similarly, the corresponding representative strain was determined with different hypothetical values of strain hardening exponent in the range of 0–0.6. Through modulating assumed strain hardening exponent values to make the computed unloading curve coincide with that of the experiment, the real strain hardening exponent was acquired. Once the strain hardening exponent was determined, the initial yield stress σy of metals could be obtained by the power law constitution. The validity of the proposed methodology was verified by three real metals: AISI 304 steel, Fe and Al alloy.

Effect of surface roughness in the determination of the mechanical properties of material using nanoindentation test

A quantitative model is proposed for the estimation of macro-hardness using nanoindentation tests. It decreases the effect of errors related to the non-reproducibility of the nanoindentation test on calculations of macro-hardness by taking into account the indentation size effect and the surface roughness. The most innovative feature of this model is the simultaneous statistical treatment of all the nanoindentation loading curves. The curve treatment mainly corrects errors in the zero depth determination by correlating their positions through the use of a relative reference. First, the experimental loading curves are described using the Bernhardt law. The fitted curves are then shifted, in order to simultaneously reduce the gaps between them that result from the scatter in the experimental curves. A set of shift depths, Δhc , is therefore identified. The proposed approach is applied to a large set of TiAl6V4 titanium-based samples with different roughness levels, polished by eleven silicon carbide sandpapers from grit paper 80 to 4,000. The result reveals that the scatter degree of the indentation curves is higher when the surface is rougher. The standard deviation of the shift Δhc is linearly connected to the standard deviation of the surface roughness, if the roughness is high-pass filtered in the scale of the indenter (15 µm). Using the proposed method, the estimated macro-hardness for eleven studied TiAl6V4 samples is in the range of 3.5-4.1 GPa, with the smallest deviation around 0.01 GPa, which is more accurate than the one given by the Nanoindentation MTS™ system, which uses an average value (around 4.3 ± 0.5 GPa). Moreover, the calculated Young's modulus of the material is around 136 ± 20 GPa, which is similar to the modulus in literature.