Adiabatic shear sensitivity of ductile metal based on gradient-dependent JOHNSON-COOK model

Based on the expression proposed by WANG for the local plastic shear deformation distribution in the adiabatic shear band（ASB） using gradient-dependent plasticity,the effects of 10 parameters on the adiabatic shear sensitivity were studied.The experimental data for a flow line in the ASB obtained by LIAO and DUFFY were fitted by use of the curve-fitting least squares method and the proposed expression.The critical plastic shear strains corresponding to the onset of the ASB for Ti-6Al-4V were assessed at different assigned ASB widths.It is found that the proposed expression describes well the non-linear deformation characteristics of the flow line in the ASB.Some parameters in the JOHNSON-COOK model are back-calculated using different critical plastic shear strains.The adiabatic shear sensitivity decreases as initial static yield stress,work to heat conversion factor and strain-rate parameter decrease,which is opposite to the effects of density,heat capacity,ambient temperature and strain-hardening exponent.The present model can predict the ASB width evolution process.The predicted ASB width decreases with straining until a stable value is reached.The famous model proposed by DODD and BAI only can predict a final stable value.

Adiabatic shear localization evolution for steel based on the Johnson-Cook model and gradient-dependent plasticity

Gradient-dependent plasticity is introduced into the phenomenological Johnson-Cook model to study the effects of strainhardening, strain rate sensitivity, thermal-softening, and microstructure. The microstructural effect （interactions and interplay among microstructures） due to heterogeneity of texture plays an important role in the process of development or evolution of an adiabatic shear band with a certain thickness depending on the grain diameter. The distributed plastic shear strain and deformation in the shear band are derived and depend on the critical plastic shear strain corresponding to the peak flow shear stress, the coordinate or position, the internal length parameter, and the average plastic shear strain or the flow shear stress. The critical plastic shear strain, the distributed plastic shear strain, and deformation in the shear band are numerically predicted for a kind of steel deformed at a constant shear strain rate. Beyond the peak shear stress, the local plastic shear strain in the shear band is highly nonuniform and the local plastic shear deformation in the band is highly nonlinear. Shear localization is more apparent with the increase of the average plastic shear strain. The calculated distributions of the local plastic shear strain and deformation agree with the previous numerical and experimental results.

INVESTIGATION ON GRADIENT-DEPENDENT NONLOCAL CONSTITUTIVE MODELS FOR ELASTO-PLASTICITY COUPLED WITH DAMAGE

Firstly, typical) gradient-dependent nonlocal inelastic models were briefly reviewed. Secondly, based on the principle of ‘gradient-dependent energy dissipation', a gradient-dependent constitutive model for plasticity coupled with isotropic damage was presented in the framework of continuum thermodynamics. Numerical scheme for calculation of Laplacian term of damage field with the numerical results obtained by FEM calculation was proposed. Equations have been presented on the basis of Taylor series for both 2-dimensional and 3-dimensional cases, respectively. Numerical results have indicated the validity of the proposed gradient-dependent model and corresponding numerical scheme.

Fishery analysis using gradient-dependent optimal interpolation

The current lack of high-precision information on subsurface seawater is a constraint in fishery research.Based on Argo temperature and salinity profiles,this study applied the gradient-dependent optimal interpolation to reconstruct daily subsurface oceanic environmental information according to fishery dates and locations.The relationship between subsurface information and matching yellowfin tuna(YFT)in the western and central Pacific Ocean(WCPO)was examined using catch data from January 1,2008 to August 31,2017.The seawater temperature and salinity results showed differences of less than±0.5°C and±0.01 compared with the truth observations respectively.Statistical analysis revealed that the most suitable temperature for YFT fishery was 28–29°C at the near-surface.The most suitable salinity range for YFT fishery was 34.5–36.0 at depths shallower than 300 m.The suitable upper and lower bounds on the depths of the thermocline were 90–100 m and 300–350 m,respectively.The thermocline characteristics were prominent,with a mean temperature gradient exceeding 0.08°C/m.These results indicate that the profiles constructed by gradient-dependent optimal interpolation were more accurate than those of the nearest profiles adopted.

An effective method for improving the accuracy of Argo objective analysis

Based on the optimal interpolation objective analysis of the Argo data, improvements are made to the em- pirical formula of a background error covariance matrix widely used in data assimilation and objective anal- ysis systems. Specifically, an estimation of correlation scales that can improve effectively the accuracy of Ar- go objective analysis has been developed. This method can automatically adapt to the gradient change of a variable and is referred to as ＂gradient-dependent correlation scale method＂. Its effect on the Argo objective analysis is verified theoretically with Gaussian pulse and spectrum analysis. The results of one-dimensional simulation experiment show that the gradient-dependent correlation scales can improve the adaptability of the objective analysis system, making it possible for the analysis scheme to fully absorb the shortwave information of observation in areas with larger oceanographic gradients. The new scheme is applied to the Argo data obiective analysis system in the Pacific Ocean. The results are obviously improved.

Effect of Relative Stress on Post-Peak Uniaxial Compression Fracture Energy of Concrete

Fracture energy in strain softening regime was investigated analytically by considering microstructures interaction and interplay.Based on gradient-dependent plasticity, the thickness of localized band was determined completely and strictly by characteristic length in relation to average grain diameter.After obtaining the plastic shear displacement of the band,the formula on axial response of concrete was proposed and the analytical post-peak fracture energy was deduced.A comparison between present theoretical results and earlier experimental results was carried out and the analytical result is reasonable and has a plausible foundation as considering the localized failure theoretically.Decreasing the relative stress leads to increasing the fracture energy non-linearly.The larger the shear elastic modulus and shear softening modulus,the lower the post-peak fracture energy.A larger fracture energy is caused by a larger thickness of shear band or a larger characteristic length of concrete material.If the inclination angle of the shear band and the compressive strength are not concerned with structural size of specimen,the post-peak fracture energy is size independent.

Adiabatic Shear Localization for Steels Based on Johnson-Cook Model and Second-and Fourth-Order Gradient Plasticity Models

To consider the effects of the interactions and interplay among microstructures, gradient-dependent models of second- and fourth-order are included in the widely used phenomenological Johnson-Cook model where the effects of strain-hardening, strain rate sensitivity, and thermal-softening are successfully described. The various parameters for 1006 steel, 4340 steel and S-7 tool steel are assigned. The distributions and evolutions of the local plastic shear strain and deformation in adiabatic shear band （ASB） are predicted. The calculated results of the second- and fourth- order gradient plasticity models are compared. S-7 tool steel possesses the steepest profile of local plastic shear strain in ASB, whereas 1006 steel has the least profile. The peak local plastic shear strain in ASB for S-7 tool steel is slightly higher than that for 4340 steel and is higher than that for 1006 steel. The extent of the nonlinear distribution of the local plastic shear deformation in ASB is more apparent for the S-7 tool steel, whereas it is the least apparent for 1006 steel. In fourth-order gradient plasticity model, the profile of the local plastic shear strain in the middle of ASB has a pronounced plateau whose width decreases with increasing average plastic shear strain, leading to a shrink of the portion of linear distribution of the profile of the local plastic shear deformation. When compared with the sec- ond-order gradient plasticity model, the fourth-order gradient plasticity model shows a lower peak local plastic shear strain in ASB and a higher magnitude of plastic shear deformation at the top or base of ASB, which is due to wider ASB. The present numerical results of the second- and fourth-order gradient plasticity models are consistent with the previous numerical and experimental results at least qualitatively.

Shear stress distribution and characteristics of deformation for shear band-elastic body system at pre-peak and post-peak

The distributed shear stress and the displacement across shear band, the evolution of plastic zones, and the load-carrying capacity of rock specimen were investigated in plane strain direct shear test according to Fast Lagrangian Analysis of Continua （FLAC）. And then the shear displacement distribution in normal direction of system composed of localized shear band and elastic rock was analyzed based on gradient-dependent plasticity. The adopted failure criterion was a composite of Mohr-Coulomb criterion, that is, the relation between tension cut-off and postpeak constitutive of rock was linear strain-softening. Numerical results show that shear stress field approximately undergoes three different stages. At first, shear stress is only concentrated in the middle of top and base of specimen. Next, shear stress in the middle of specimen tends to increase, owing to superposition of shear stresses. Interestingly, two peaks of shear stress appear far from the loading ends of specimen, and the peaks approach with the increase in timestep until elements at the center of specimen yield. Finally, relatively lower shear stress level is reached in large part of specimen except in the regions near the two ends. As flow stress decreases, the analytical shear displacement distribution in shear band based on gradient-dependent plasticity becomes steeps outside the band, it is linear and its slope tends to decrease. These theoretical results qualitatively agree with that of the present numerical predicted results. Main advantage of the analytical solution over the numerical results according to FLAC is that it is continuous, smooth and non-linear （except at elastic stage）.

Non-Local Analysis of Forming Limits of Ductile Material Considering Void Growth

The current study performed a finite element analysis of the strain localization behavior of a voided ductile material using a non-local plasticity formulation in which the yield strength depends on both an equivalent plastic strain measurement (hardening parameter) and Laplacian equivalent. The introduction of gradient terms to the yield function was found to play an important role in simulating the strain localization behavior of the voided ductile material. The effect of the mesh size and characteristic length on the strain localization were also investigated. An FEM simulation based on the proposed non-local plasticity revealed that the load-strain curves of the voided ductile material subjected to plane strain tension converged to one curve, regardless of the mesh size. In addition, the results using non-local plasticity also exhibited that the dependence of the deformation behavior of the material on the mesh size was much less sensitive than that with classical local plasticity and could be successfully eliminated through the introduction of a large value for the characteristic length.