Value Of Equivalent Plastic Strain Research Articles

Cavern spacing of CAES cavern group in hard rock based on plastic zone and deformation analysis

Existing research on layout parameters of compressed air energy storage (CAES) cavern groups in hard rock has indicated that the key influential factors for group stability include buried depth, diameter, and cavern spacing. Among these, in contrasting to other factors, the research on cavern spacing is limited. This paper focuses on the issue of safe spacing and proposes a numerical method to determine it. By establishing a series of finite element models, the stress state of surrounding rock, changes in shape, equivalent plastic strain of plastic zone, and cavern wall deformation under different spacing have been studied. When a group of air storage caverns in rows is subjected to high internal pressure, for a small spacing, the plastic zone of the surrounding rock between two caverns is connected. Here, the size of the plastic zone, equivalent plastic strain value, and deformation of the cavern wall are relatively large, making the surrounding rock highly susceptible to damage. As the spacing increases, the horizontal width of the plastic zone, the maximum equivalent plastic strain value, the displacement changes of the cavern wall remain stable. This spacing is virtually the same as that when the plastic zone of the surrounding rock is no longer connected and can be selected as a safe spacing. This study explores the design of cavern safe spacing of underground CAES cavern groups and discusses several influencing factors, which can provide references for follow-up energy storage engineering and research.

Ductile fracture of high-strength bolts under combined actions at elevated temperatures

Steel bolted connections are critical structural components that can initiate progressive collapse at ambient and elevated temperatures. High-strength bolts are highly vulnerable members due to rapid strength degradation at high temperatures. This paper presents a numerical study on the ductile fracture of the frequently used Grade 8.8 and 10.9 structural bolts under tension, shear, and combined forces at 20–700 °C. True stress–strain curves have been defined up to fracture for both grades. The fracture parameters have been calibrated by a total of four experiments: two tensile and shear tests for each grade. The ductile fracture models with proposed fracture parameters have been further validated by pretensioned shear tests at elevated temperatures. The relationship between equivalent strain and triaxiality was investigated based on the numerical results. In general, equivalent plastic strain values become larger with increasing temperature. The fracture analysis with given ductile fracture parameters estimates the test results with reasonable accuracy under all failure modes. The fracture model can be used in numerical analysis to investigate the ductile failure of the high-strength bolted connections at ambient and elevated temperatures. Furthermore, the influence of displacement at fracture values on the results was investigated by a three-bolted inclined shear test.

On deformation characterisation of machined surfaces and machining-induced white layers in a milled titanium alloy

Machining-induced white layers and severely deformed layers are undesirable surface integrity features which can be formed when machining high-strength aerospace alloys. An orthogonal milling process has been designed and performed to assess the impact of cutting speeds, tool wear, cutting edge radius and climb vs conventional milling on white layer formation and plastic strain distribution. The plastic deformation in the machined surface associated with the formation of white layers in Ti-6Al-4V has been quantified using micro-grids of different length scales printed using the electron beam lithography technique. It was found that white layers formed via the severe plastic deformation mechanism, at equivalent plastic strain values in excess of 1.2 and in regions of the cutting arc with the instantaneous chip thickness of less than the cutting-edge radius and ploughing and rubbing being the dominant mechanisms. The results indicated that the magnitude of the measured strains and the depth of plastically deformed material was greater at lower cutting speeds, during climb milling and when machining with a larger cutting edge radius and tool flank wear land.

Force Controlled Low Cycle Fatigue (LCF) Life Evaluation Methodology Based on Unstabilized Material Properties

Low Cycle Fatigue (LCF) is a prominent failure mechanism in many design components; therefore, an evaluation of cycles to failure in this regime is of high importance. Most international standards recommend a closed loop strain-controlled mode specimen testing in this regime. However, the ꜪN data obtained from this test is not suitable for life evaluation of parts enduring force-controlled history during actual service without correction for control mode. Many existing procedures, which accounts for cyclic strain stabilization during force-controlled loading may significantly complicate the finite elements analysis (FEA) at solving or post processing stages and are often an inherent source of uncertainty. A heuristic, cost effective and sufficiently accurate approach for LCF life estimation is advocated. The method involves only two force loading FEA simulations, one of the actual parts and the other of the test specimen, using initial unstabilized stress strain curve, followed by a limited number of force-controlled specimens testing. Actual part and specimen life correlation performed using first loading unstabilized equivalent plastic strain value Ꜫp1 under locality and similitude assumptions. Unstabilized strain vs. number of cycles to failure curve Ꜫp1N is constructed and discussion regarding specimen geometry considerations for providing sufficient accuracy is included. Method validation and crack propagation study are provided.

Numerical Methodology for Aerostructures Hail Impact Damage Prediction

The two numerical approaches for modelling of soft-body impact in Abaqus/Explicit have been applied in this work for prediction of high-velocity hail impact damage in aeronautical structures. The applied methods are the CEL (Coupled Eulerian Lagrangian) and SPH (Smoothed Particle Hydrodynamics), while the impacted structure is a metallic slat structure. Comparison of the CEL and SPH methods has been performed by impact simulations at a rigid plate, aimed to validate the applied material model, and by simulation of the slat structure impact. Two material models have been applied to study the effect of high strain-rates at the damage process in the metallic structure. The first is the standard isotropic plasticity model that defines material failure based on the value of equivalent plastic strain. The second constitutive model in the analyses is the Johnson-Cook model that includes the effects of strain rate and temperature on the material failure process. The simulations have been stable, illustrating the robustness of Abaqus/Explicit in these highly nonlinear impact cases. Compared to the CEL, the SPH method is computationally more efficient.

Finite element analysis of plastic deformation in shear punch test

Strain level and mode of deformation in shear punch testing (SPT) was investigated by finite element method (FEM). The value of equivalent plastic strain was related to the punch displacement (d), punch-die clearance (W), and sample thickness (t) by the relationship of ε∝d/tW. Based on the numerical simulation, it was inferred that the deformation mode depends on the clearance and thickness. It was shown that W/t = 0.1 corresponds to the pure shear mode for AISI 304L austenitic stainless steel, for which the axial components of the plastic strain tend to zero. These findings were found to be consistent with experimental observations and can be utilized in future studies on the mechanical properties and microstructure evolution of materials.

Experimental and numerical study on largely perforated steel shear plates with rectangular tube–shaped links

Steel plate shear wall is one of the most effective dissipation systems which are commonly used in buildings. In order to improve the hysteretic behavior of shear panels, large perforation patterns may be applied, transforming the shear plate into a sort of grid systems, where plastic deformations are concentrated on specific internal link elements. This study investigates the behavior of grid systems loaded in shear where the internal links are created by cutting out internal parts, leaving rectangular tube–shaped link elements. The influence of internal link geometry on the cyclic performance of the systems is investigated experimentally. To this purpose, two specimens that varied in the width of links were fabricated and tested. The results indicate that any increase in the width of links leads to the growth of the ultimate strength, stiffness, and energy absorption capacity. Likewise, the stress distribution and fracture tendency of the tested specimens have been simulated by the finite element software (ABAQUS) and validated according to the experimental results. Based on finite element results, a suitable analytical formulation for the prediction of the shear strength at several shear deformation demands, considering the effect of thickness of the link, has been provided. Moreover, to improve the fracture tendency of the specimens, butterfly-shaped links, which varied in the middle length, were applied. The obtained results, which have been interpreted by considering the equivalent plastic strain value, prove that the shear panel behavior improves significantly when butterfly-shaped links are considered.

Effect of Temperature on Strength and Hardness in Multi-pass Equal Channel Angular Pressing (ECAP) of Aluminum Alloys

In the Equal channel angular pressing (ECAP) process, the sample passes through the channel and the shear stress applied to the sample leads to grain refinement and consequently, the mechanical properties of the sample will be increased. In this article, the effect of implementing the ECAP process at elevated temperature on the strength and hardness of the samples will be studied. Commercially pure (99.0% Al) and AA6063 aluminum round bars are prepared and ECAPed in a die with channel angle of $$\phi$$ = 120° and a corner angle of $$\varphi$$ = 20°. The tensile strength and hardness are compared for 1–8 pass ECAPed samples at 150 °C and room temperature. Also, the ECAP process is modeled in a finite element software to predict the plastic strain distribution in repetitive passes of ECAP. The results show that performing ECAP at elevated temperature decreases the tensile strength by about 5% and 12% in the AA6063 and commercially pure aluminum alloy samples, respectively. Also, at 150 °C, the percent of the increase in the tensile strength decreases in pass #1 but at pass #8 of ECAP, the percent of increase in the tensile strength is equal. So, decrease in the tensile strength in initial passes cannot be compensated by repetition of the ECAP process and at higher passes the strain saturation does not allow to recompense the decrease in the strength at initial passes. The finite element results show that the plastic strain heterogeneity and the value of equivalent plastic strain obtained from FEM are comparable with analytical formulations proposed by other researchers with acceptable error.

Equal channel angular pressing of the aluminium alloy: A numerical investigation

Equal channel angular pressing (ECAP) is adopted as the most popular bulk severe plastic deformation (SPD) processing technique and has been utilised for the grain refinement in several metals and alloys. The aforesaid technique, in which the metallic billet processes through a simple shear was investigated by finite element analysis in this work. The die channel angle for the investigation was selected by considering the minimum energy consumption for the induction of maximum uniform strain. Out of preferred channels, 110° was found suitable. Al-6063 was considered as work material. Maximum load requirement for accomplishing the operation, effective stress and strain distribution were also inquired. The mathematically calculated equivalent plastic strain value found in close proximity to the value obtained from the FEA. In the process die channel angle and friction conditions are primarily responsible for maximum strain induction in the work material, which was affirmed here by the numerical analysis. In addition to it these two parameters influence the maximum load requirement for accomplishing the operation whereas, ram rate within the investigated range has the negligible impact.

Shear test-based identification of hardening behaviour of stainless steel sheet after onset of necking

In the metal sheet-forming process, localised thinning immediately before failure is a rapid and intensive process. This paper discusses such intensive thinning and elaborates on the importance of the hardening behaviour at large plastic strains. In particular, for the reliable prediction of intensive sheet-thinning evolution, an accurate determination of the hardening behaviour is important; however, the identification cannot be performed using classical uniaxial tests owing to necking. Therefore, this paper describes the development of a new shear specimen that provides enough data for hardening curve characterisation up to an equivalent plastic strain value that is twice that in a tensile test. After characterisation, based on the inverse identification procedure, two verification cases confirmed the identified data. Both cases are typically considered stochastic processes, and they exhibit a large scatter in the experimental testing: Necking evolution in a uniaxial case and localisation evolution of a notched specimen. However, the verification analyses confirm that both processes are deterministic, and a good prediction could be reached exclusively by a precise identification of the hardening behaviour at large plastic strains.

Fracture behaviour and numerical study of resistance spot welded joints in high-strength steel sheet

Cross tension tests of resistance spot welded joints with varying nugget diameter were carried out using 980 MPa high strength steel sheet of 1.6 mm thickness. In proportion, as nugget diameter increased from 3√t to 5√t (where t is thickness), cross tension strength (CTS) increased while fracture morphology simultaneously transferred from interface fracture to full plug fracture. In cases of interface fracture, circumferential crack initiation due to separation of the corona bond arose at an early stage of loading. The crack opening process without propagation was recognized until just before fracture and then the crack propagated to the nugget immediately in a brittle manner around CTS. In full plug fracture, main ductile crack initiation from the notch-like part at the end of sheet separation occurred with the sub-crack initiated at an early stage. The ductile crack propagated toward the HAZ and base material to form full plug fracture. The mode I stress intensity factor was considered as a suitable fracture parameter because the circumferential crack behaved pre-crack for brittle fracture in the nugget region at the final stage. Based on the FE analysis, the mode I stress intensity factor was calculated as 116 MPa √m at CTS as fracture toughness for the nugget. With respect to full plug fracture, ductile crack initiation behaviour from the notch-like part was expressed by concentration of equivalent plastic strain. On the assumption that the ductile crack arose in critical value of equivalent plastic strain, the value was calculated as 0.34 by FE analysis. Reasonable interpretation for interface fracture and full plug fracture in the resistance spot welded joint was proposed due to first crack initiation by stress concentration, brittle fracture by using mode I stress intensity factor, and ductile crack initiation by using equivalent plastic strain.

A finite element study on effect of frictional heating in the taylor rod impact problem

In an impact phenomenon the material is subjected to very short duration high force levels resulting large plastic deformations and rise in temperature at high strain rates. A circular rod impacting against a rigid surface called as Taylor rod impact test is widely used for determining the mechanical behaviour of materials subjected to high strain rates with associated increase in temperature. A three-dimensional large deformation, thermo-elasto-plastic, dynamic, contact, finite element formulation is developed to study the effect of temperature rise due to plastic deformation and surface friction on the deformation and stress fields. It is found that the predicted equivalent plastic strain values are influenced by temperature generated due to plastic deformation and surface friction. The values of the coefficient of friction have a profound effect on the location of fracture initiation on the impacting face in a circular rod.

A Generalized Critical Velocity Window Based on Material Property for Cold Spraying by Eulerian Method

In this paper, the previously developed Eulerian model (Yu et al., J Therm Spray Technol 21(3):745-752, 2012), which could well predict the critical velocity and erosion velocity, was extended to other commonly used materials such as aluminum, iron, nickel, stainless steel 316, and Inconel718 for studying the influence of material property and establishing a generalized window of critical velocity. Results show that the deformation behavior of the used materials could be classified as coordinated deformation (copper, iron, nickel) and uncoordinated deformation patterns (aluminum, stainless steel, and Inconel718). However, it was found that the steady maximum equivalent plastic strain values at the critical velocity for each material concentrate in the extent of 2.6-3.0 regardless of deformation pattern. Dimensionless analysis shows that, the calculated critical velocity increases with the increase of material characteristic velocity, and this relationship can be primarily used to predict the critical velocity.

Numerical Simulation of Aluminum Alloy Wheel 13° Impact Test Based on Abaqus

In order to predict the result of impact test in the design phase and reduce the experimental times, which can save cost and shorten development cycle, a finite element model of aluminum alloy wheel 13-degree impact test is established based on Abaqus. All mechanical parts such as the standard impact block, the assembly of the wheel and the tire, the support and bolts are included in the finite element model. The predicted result of finite element analysis and the experimental result agree very well shows the finite element model is correct. The equivalent plastic strain value was also put forward as fracture criterion for the wheel in the impact test which realizes the transition from the qualitative analysis to the quantitative analysis in the development process of aluminum alloy wheel.

External force-assisted laser forming process for gaining high bending angles

Laser forming process is used in forming and bending of metallic and non-metallic sheets. Laser beam irradiation causes a localized temperature increase and a localized mechanical strength decrease. In this article, an external mechanical force is added to a laser beam irradiation, which is called external force-assisted laser forming process, to gain a 90-degree bending angle. Furthermore, Numerical simulation of the process is performed to achieve a good understanding of the process. Simulation results show that more than two-third of the final forming is due to the laser beam irradiation. Equivalent plastic strain values during laser forming and external force-assisted laser forming processes are compared. Results show that equivalent plastic strain in laser forming process increases in a step pattern, with increasing in scan pass numbers. This occurs because when the laser beam irradiates on the sheet surface, it reduces the yield strength of the sheet. Equivalent plastic strain in external force-assisted laser forming process has an oscillatory step nature. This attributes to simultaneous effects of strain hardening and thermal induced reduction of yield strength of the sheet. Simulations were in good accordance with experiments.

Investigation of the effects of perturbation forces to buckling in internally pressurized torispherical pressure vessel heads

The object of this paper is to investigate the effects of perturbation forces to buckling in pressure vessel heads. The pressure vessel heads in concern are confined to torispherical geometry with thin walls. Perturbation forces can alter not only the critical load for buckling but the buckled shape as well. In this paper in addition to previously used perturbation model, three more different perturbation force configurations are applied to the knuckle of the vessel. Internally pressurized three-dimensional torispherical pressure vessel head model that is previously used in literature is constructed and finite element program ANSYS Workbench is used for the solutions. First of all eigenvalue solutions are performed for each model. Then nonlinear instability solutions are conducted to obtain more realistic instability pressure values. For the nonlinear analyses not only large deformation static analyses but also large deformation transient analyses are conducted. For nonlinear analyses, perfectly plastic material model is used. It is concluded that instability pressures obtained by transient analyses are closer to plastic pressure values by PWC and ASME TES criteria and perturbation models increase instability pressure and equivalent plastic strain values.

Equal‐channel multiangular extrusion of semicrystalline polymers

AbstractPotentialities of a new simple shear‐based scheme of the solid‐phase extrusion of polymers, named the equal channel multiple angular extrusion (ECMAE), for modification of semicrystalline polymer structure have been investigated by the example of low‐ and high‐density polyethylene (LDPE, HDPE), polyamide‐6 (PA‐6), and polytetrafluoroethylene (PTFE). The effects of velocity and extrusion temperature, plastic deformation intensity, and accumulated equivalent plastic strain value on properties of a number of crystallizing polymers have been studied. It has been shown that the highest strength characteristics are attained for the extrusion temperatures of (0.8–0.95) of the melting temperature and deformation velocity of (0.6–1.1) mm s−1. For the ECMAE‐processed specimens, the density, the enthalpy, and the melting temperature have become higher. In the oriented structure of semicrystalline polymers formed by the ECMAE, the lamellae are oriented along the extrudate axis. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers

The effect of undermatching on crack tip constraint in a welded structure of nodular irons

Abstract The main aim of this paper is to investigate the effect of yield strength mismatch of parent and weld metal on the fracture behavior of plain and heat-treated welded nodular cast iron. For this, experimental and theoretical studies were performed. Nickel electrode, which has lower yield strength value than that of the parent material, was used to join nodular cast iron by cold arc welding method. In experimental study, fracture toughness (J-integral) values were determined for various crack locations including base, weld metal and heat affected zone. In theoretical study, finite element analyses were performed for the same crack locations with different crack lengths. Stress triaxiality and equivalent plastic strain values were determined for all crack locations and various crack lengths. Finally, fracture toughness values of the base metal were determined as lower than those of the other regions including the weld metal and the heat affected zones. Stress triaxiality and equivalent plastic strain values used to clarify the effect of yield strength mismatch on the constraint around crack tip increased with growing crack length in annealed and under-matched models. In annealed models, stress triaxiality values became slightly lower but equivalent plastic strain values appeared higher than those of under-matched models.

Transferability of critical condition for ductile cracking in bent small scale specimen to evaluation of critical internal pressure for ductile cracking in axially notched linepipe

For two types of API 5L X65 linepipes, the critical conditions for ductile cracking of the linepipe steel and their applicability to the evaluation of the ductile cracking of an axially notched linepipe were investigated. Static three point bending tests and finite element (FE) analyses for a Charpy V notch specimen were conducted to evaluate the critical conditions for ductile cracking from the notch tip. At the position of ductile cracking for the Charpy specimen, the calculated stress triaxiality was almost constant for both linepipe steels; however, the equivalent plastic strain for each linepipe steel was different. Hydrostatic burst tests were then conducted for internally patched linepipes with an axial through wall notch. The results of FE analyses for the hydrostatic burst tests indicated that the maximum equivalent plastic strain value within the wall thickness was almost the same as that obtained from the three point bending test in the Charpy V notch specimen. It was therefore ascertained that the critical conditions for ductile cracking of linepipes with an actual notch can be predicted from the results of a small scale test and FE analysis, which are used to evaluate the relationship between the stress triaxiality and the equivalent plastic strain.

An eulerian finite-element model for determination of deformation state of a copper subjected to orthogonal cutting

An Eulerian finite-element (FE) model was developed to predict the stress and strain distributions in the material subjected to the orthogonal machining process. Metallographic sections taken from commercially pure copper samples and subjected to orthogonal cutting were examined to determine the local strain gradients generated in the material ahead of the cutting tool tip. Local flow stress values were estimated from the microhardness measurements. Experimental flow stress and equivalent plastic strain values were found to obey a Voce-type exponential relationship, which was used in the development of the material model for the numerical simulations. The sizes of both the primary deformation zone (350 µm) and the secondary deformation zone (50 µm) predicted by the numerical model were in agreement with the experimental observations. The experimental results showed that the equivalent strain was 3.65 in the material 50 µm directly ahead of the tool tip, which compared well with the numerically observed strain (3.50). According to the numerical observations, along the primary shear plane, the high tool tip stress of 410 MPa decreased to 260 MPa near the chip root. Numerical and experimental stress and strain distributions correlated well in terms of both magnitudes and distributions, indicating that the application of an Eulerian FE approach served to predict the deformation state of the material ahead of the tool tip successfully.