The Effect of Rate Dependence on Localization of Deformation and Failure in Softening Solids

2015 ◽  
Vol 82 (2) ◽  
Author(s):  
Alan Needleman
Keyword(s):  
Carrying Capacity ◽  
Constitutive Relations ◽  
Rate Sensitivity ◽  
Complete Loss ◽  
Fixed Rate ◽  
Deformation And Failure ◽  
Localization Of Deformation ◽  
Rate Dependent ◽  
Plastic Dissipation ◽  
Viscoplastic Solid

Localization of deformation and failure, a complete loss of stress carrying capacity, is studied for two rate dependent constitutive relations: (i) a Kelvin–Voigt solid and (ii) a viscoplastic solid. A planar block infinite in one direction is subjected to monotonically increasing shear displacements at a fixed rate. Geometry changes are neglected and attention is confined to quasi-static loading conditions. For the Kelvin–Voigt solid, localization precedes failure if there is hardening outside the band and softening inside the band while failure precedes localization if there is softening both inside and outside the band. For the viscoplastic solid, localization precedes failure when there is softening inside the band regardless of the sign of the hardening parameter outside band. For the Kelvin–Voigt solid, it is found that the localization time (or strain) varies logarithmically with the band thickness for small values of band thickness while the time (or strain) to a complete loss of stress carrying capacity has, in general, a different scaling with band thickness. For the viscoplastic solid, with plastic dissipation outside the band as well as inside the band, the strain and the total plastic dissipation to failure are nearly independent of band thickness for sufficiently small thickness values, with what is sufficiently small decreasing with decreasing rate sensitivity. Possible implications for grid based modeling of localization and failure are discussed.

Numerical Analysis of Plane-Strain Tension Test for Rate-Dependent Solids

1992 ◽  
Vol 59 (3) ◽  
pp. 485-490 ◽  
Author(s):  
P. Tugˇcu
Keyword(s):  
Numerical Analysis ◽  
Strain Rate ◽  
Plane Strain ◽  
Rate Sensitivity ◽  
Tension Test ◽  
Engineering Strain ◽  
Plane Strain Tension ◽  
Rate Dependent ◽  
Strain And Strain Rate ◽  
Strain Rate Hardening

The plane-strain tension test is analyzed numerically for a material with strain and strain-rate hardening characteristics. The effect of the prescribed rate of straining is investigated for an additive logarithmic description of the material strain-rate sensitivity. The dependency to the imposed strain rate so introduced is shown to have a significant effect on several features of the load-elongation curve such as the attainment of the load maximum, the onset of localization, and the overall engineering strain.

scholarly journals Strain-Rate-Dependent Deformation Behavior and Mechanical Properties of a Multi-Phase Medium-Manganese Steel

Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 344 ◽  
Author(s):  
Simon Sevsek ◽  
Christian Haase ◽  
Wolfgang Bleck
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Deformation Behavior ◽  
Rate Sensitivity ◽  
Manganese Steel ◽  
Strain Rates ◽  
Rate Dependent ◽  
Medium Manganese Steel ◽  
Multi Phase

The strain-rate-dependent deformation behavior of an intercritically annealed X6MnAl12-3 medium-manganese steel was analyzed with respect to the mechanical properties, activation of deformation-induced martensitic phase transformation, and strain localization behavior. Intercritical annealing at 675 °C for 2 h led to an ultrafine-grained multi-phase microstructure with 45% of mostly equiaxed, recrystallized austenite and 55% ferrite or recovered, lamellar martensite. In-situ digital image correlation methods during tensile tests revealed strain localization behavior during the discontinuous elastic-plastic transition, which was due to the localization of strain in the softer austenite in the early stages of plastic deformation. The dependence of the macroscopic mechanical properties on the strain rate is due to the strain-rate sensitivity of the microscopic deformation behavior. On the one hand, the deformation-induced phase transformation of austenite to martensite showed a clear strain-rate dependency and was partially suppressed at very low and very high strain rates. On the other hand, the strain-rate-dependent relative strength of ferrite and martensite compared to austenite influenced the strain partitioning during plastic deformation, and subsequently, the work-hardening rate. As a result, the tested X6MnAl12-3 medium-manganese steel showed a negative strain-rate sensitivity at very low to medium strain rates and a positive strain-rate sensitivity at medium to high strain rates.

Osmo-inelastic response of the intervertebral disc annulus fibrosus tissue

2020 ◽  
Vol 234 (9) ◽  
pp. 1000-1010
Author(s):  
Amil Derrouiche ◽  
Ameni Zaouali ◽  
Fahmi Zaïri ◽  
Jewan Ismail ◽  
Zhengwei Qu ◽  
...  
Keyword(s):  
Intervertebral Disc ◽  
Annulus Fibrosus ◽  
Mechanical Response ◽  
Rate Sensitivity ◽  
Image Correlation ◽  
Inelastic Response ◽  
Full Field ◽  
Osmotic Effect ◽  
Rate Dependent ◽  
Optical Strain

The aim of this article is to provide some insights on the osmo-inelastic response under stretching of annulus fibrosus of the intervertebral disc. Circumferentially oriented specimens of square cross section, extracted from different regions of bovine cervical discs (ventral-lateral and dorsal-lateral), are tested under different strain-rates and saline concentrations within normal range of strains. An accurate optical strain measuring technique, based upon digital image correlation, is used in order to determine the full-field displacements in the lamellae and fibers planes of the layered soft tissue. Annulus stress–stretch relationships are measured along with full-field transversal strains in the two planes. The mechanical response is found hysteretic, rate-dependent and osmolarity-dependent with a Poisson’s ratio higher than 0.5 in the fibers plane and negative (auxeticity) in the lamellae plane. While the stiffness presents a regional-dependency due to variations in collagen fibers content/orientation, the strain-rate sensitivity of the response is found independent on the region. A significant osmotic effect is found on both the auxetic response in the lamellae plane and the stiffness rate-sensitivity. These local experimental observations will result in more accurate chemo-mechanical modeling of the disc annulus and a clearer multi-scale understanding of the disc intervertebral function.

Nonlinear Rate-Dependent Stress-Strain Behavior of Light-Weight Textile Conveyor Belt

2011 ◽  
Vol 675-677 ◽  
pp. 453-456
Author(s):  
Ze Xing Wang ◽  
Jin Hua Jiang ◽  
Nan Liang Chen
Keyword(s):  
Loading Rate ◽  
Testing Machine ◽  
Rate Sensitivity ◽  
Sensitivity Coefficient ◽  
Conveyor Belt ◽  
Uniaxial Tensile ◽  
Stress Strain ◽  
Strain Behavior ◽  
Rate Dependent ◽  
Dependent Behavior

In order to investigate the effect of loading rate on the tensile performance, the uniaxial tensile experiments were conducted on universal testing machine under different loading rates (5 mm/min, 10mm/min, 50 mm/min, 100 mm/min and 150 mm/min), and a constant gage length equal to 200mm, resulting in loading strain rate of 4.17×10-4, 8.33×10-4/s, 4.17×10-3/s, 8.33×10-3/s,1.25×10-2/s, and the tensile stress-strain curves were obtained. The experimental results show that the tensile properties of the conveyor belt exhibit obvious rate-dependent behavior. In this paper, the rate sensitivity coefficient varied with loading rate, was calculated, and the nonlinear rate-dependent behavior was also investigated.

Plastic deformation and fracture characteristics of Hadfield steel subjected to high-velocity impact loading

2002 ◽  
Vol 216 (10) ◽  
pp. 971-982 ◽  
Author(s):  
W-S Lee ◽  
T-H Chen
Keyword(s):  
Strain Rate ◽  
Work Hardening ◽  
Shear Bands ◽  
Rate Sensitivity ◽  
Constitutive Law ◽  
Hadfield Steel ◽  
Flow Strength ◽  
Rate Dependent ◽  
Work Hardening Rate ◽  
The Impact

Investigation of the impact behaviour of Hadfield steel has been carried out in a broad range of strain rates from 10−3 to 9 × 103s−1 by means of a servo-hydraulic machine and a compressive split Hopkinson bar. The effects of strain rate on the impact properties, substructure evolution and fracture resistance have been evaluated. The observed stress-strain response is influenced greatly by strain rate, resulting in obvious changes of work hardening rate, strain rate sensitivity and activation volume. This rate-dependent behaviour is in good agreement with model predictions using the Zerilli-Armstrong constitutive law. Dislocation tangle and deformation twin substructures are also found to develop as a function of strain rate. Increasing dislocation and twin densities enhance the work hardening rate and flow strength. Catastrophic failure at high rates results from the formation of localized shear bands. With increasing strain rate, there is an increase in brittle cleavage microfracture, resulting in ductility loss. Microcracking initiates at grain boundaries due to the presence of carbide precipitates.

Microstructural Modelling of P91 Martensitic Steel Under Uniaxial Loading Conditions

2013 ◽  
Author(s):  
Brian Golden ◽  
Dongfeng Li ◽  
Noel O’Dowd
Keyword(s):  
Power Plant ◽  
Mechanical Response ◽  
Electron Backscatter Diffraction ◽  
Voronoi Tessellation ◽  
Peak Stress ◽  
Grain Structure ◽  
Plant Materials ◽  
Deformation And Failure ◽  
Rate Dependent ◽  
Modelling Studies

The changing face of power generation requires an improved understanding of the deformation and failure response of power plant materials. Important insights can be obtained through microstructurally motivated modelling studies. This paper deals with the comparisons of predictions of the mechanical response of a power plant steel (P91), obtained from a model with a measured microstructure with those obtained from a numerically simulated microstructure. Electron backscatter diffraction (EBSD) is employed to obtain the orientation of the martensitic grain structure of the steel. This information is incorporated within a representative volume element (RVE) to represent the material microstructure. A non-linear, rate dependent, finite strain crystal plasticity model is used to represent the deformation of the material, with the orientation of each finite-element integration point determined from the EBSD analysis. The deformation under uniaxial tension is analysed. Due to the inhomogeneous microstructure strong strain gradients are generated within the RVE even under remote homogenous strain states. It is seen that peak stress/strain states are associated with particular features of the microstructure. The results taken from the model are compared with those obtained with an equiaxed microstructure generated using the Voronoi tessellation method.

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