Improved analysis method for structural members subjected to blast loads considering strain hardening and softening effects

2021 ◽  
pp. 136943322110073
Author(s):  
Liuliang Cui ◽  
Xihong Zhang ◽  
Hong Hao
Keyword(s):  
Strain Hardening ◽  
Direct Shear ◽  
Analysis Method ◽  
Analysis And Design ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Design Charts ◽  
Plastic Hardening ◽  
Elastic Perfectly Plastic ◽  
Hardening And Softening

In analysis and design of structures subjected to blast loading, equivalent Single-Degree-of-Freedom (SDOF) method is commonly recommended in design guides. In this paper, improved analysis method based on SDOF models is proposed. Both flexural and direct shear behaviors of structures subjected to blast load are studied using equivalent SDOF systems. Methods of deriving flexural and direct shear resistance functions are introduced, of which strain hardening and softening effects are considered. To collocate with the improved SDOF models, the improved design charts accounting for strain hardening and softening are developed through systematical analysis of SDOF systems. To demonstrate the effectiveness of the proposed analysis method, a model validation is made through comparing the predictions with laboratory shock tube testing results on reinforced concrete (RC) columns. It is found that compared to the conventional approach with elastic and elastic-perfectly-plastic model, the elastic-plastic-hardening model provides more accurate predictions. Additional non-dimensional design charts considering various levels of elastic-plastic-hardening/softening resistance functions are developed to supplement those available in the design guides with elastic-perfectly-plastic resistance function only, which provide engineers with options to choose more appropriate resistance functions in design analysis.

Some theoretical considerations relating to strain concentration in elastic-plastic bending of beams

1968 ◽  
Vol 3 (4) ◽  
pp. 304-312 ◽  
Author(s):  
M Radomski ◽  
D J White
Keyword(s):  
Strain Hardening ◽  
Numerical Solutions ◽  
Bending Moment ◽  
Rate Of Change ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rate Of Increase ◽  
Plastic Zones ◽  
Elastic Perfectly Plastic

Theoretical derivations are presented for the relations between maximum deflection and the corresponding maximum strain for some simple beams subject to elastic-plastic bending. Both elastic-perfectly plastic and arbitrary stress-strain relations are considered. Where possible, explicit analytical solutions are given, but where this is not possible numerical solutions are obtained by means of computer programmes. The calculations show that in elastic-perfectly plastic material short plastic zones may develop and cause large strains in the beam even though the deflection corresponding to first yield is not greatly exceeded. On the other hand, strain hardening elongates the plastic zones, so producing a more favourable strain distribution along the length of the beam than would exist without it. The more pronounced the strain-hardening characteristic, i.e. the greater the rate of increase of stress with strain, the less concentrated will be the strains. The mode of loading is important in that the higher the rate of change of bending moment, in the region of ihe maximum bending moment, the more concentrated will be the local strains.

Combined Viscous and Plastic Deformations in Two-Dimensional Large Strain Finite Element Analysis

1985 ◽  
Vol 107 (1) ◽  
pp. 13-18 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Input Parameter ◽  
Time Integration ◽  
Strain Increment ◽  
Total Strain ◽  
Two Dimensional ◽  
Elastic Plastic ◽  
Time Stepping ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Capabilities for the analysis of combined viscous and plastic behavior have been added to an existing finite element computer program for two-dimensional elastic-plastic calculations. This program (PAPSTB) has been formulated for elastic-plastic stress and deformation analyses of two-dimensional and axisymmetric structures. It has the ability to model large strains and large deformations of elastic-perfectly plastic, multi-linear hardening, or power-hardening materials. The program is based on incremental plasticity theory with a von Mises yield criterion. Time dependent behavior has been introduced into the PAPSTB program by adding a viscous strain increment to the elastic and plastic strain increment to form the total strain increment. The viscous calculations presently employ a power-law relationship between the viscous strain rate and the effective stress. The finite element code can be easily modified to handle more complex viscous models. The Newmark method for time integration is used, i.e., an input parameter is included which enables the user to vary the time domain approximation between forward (explicit) and backward (implicit) difference. Automatic time stepping is used to provide for stability in the viscous calculations. It is controlled by an input parameter related to the ratio of the current viscous strain increment to the total strain. The viscoplastic capabilities of the PAPSTB program are verified using the axisymmetric problem of an internally pressurized, thick-walled cylinder. The transient viscoplastic case is analyzed to demonstrate that the elastic-perfectly plastic solution is obtained as a steady-state condition is approached. The influence of varying the time integration parameter for transient viscoplastic calculations is demonstrated. In addition, the effects of time step on solution accuracy are investigated by means of the automatic time stepping algorithm in the program. The approach is then applied to a simple forging problem of cylinder upsetting.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 2: Analysis of Repeated Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 75-82 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Shear Strain ◽  
Element Model ◽  
Rolling Contact ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rolling Contacts ◽  
Elastic Perfectly Plastic ◽  
Multiple Translations ◽  
Contact Part

This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

Scaling of Solutions for the Lateral Buckling of Elastic-Plastic Pipelines

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Ralf Peek ◽  
Heedo Yun
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Finite Element Solution ◽  
Reference Solution ◽  
Element Solution ◽  
Lateral Buckling ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
The Moment

Analytical solutions for the lateral buckling of pipelines exist for the case when the pipe material remains in the linearly elastic range. However for truly high temperatures and/or heavier flowlines, plastic deformation cannot be excluded. One then has to resort to finite element analyses, as no analytical solutions are available. This paper does not provide such an analytical solution, but it does show that if the finite element solution has been calculated once, then that solution can be scaled so that it applies for any other values of the design parameters. Thus the finite element solution need only be calculated once and for all. Thereafter, other solutions can be calculated by scaling the finite element solution using simple analytical formulas. However, the shape of the moment-curvature relation must not change. That is, the moment-curvature relation must be a scaled version of the moment-curvature relation for the reference problem, where different scale factors may be applied to the moment and curvature. This paper goes beyond standard dimensional analysis (as justified by the Bucklingham Π theorem), to establish a stronger scalability result, and uses it to develop simple formulas for the lateral buckling of any pipeline made of elastic-plastic material. The paper includes the derivation of the scaling result, the application procedure, the reference solution for an elastic-perfectly plastic pipe, and an example to illustrate how this reference solution can be used to calculate the lateral buckling response for any elastic-perfectly plastic pipe.

Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Phuong H. Hoang ◽  
Kunio Hasegawa ◽  
Bostjan Bezensek ◽  
Yinsheng Li
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Large Strain ◽  
Bending Moment ◽  
Limit Load ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Weighted Factor ◽  
Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

Junction Growth and Energy Dissipation at the Very Early Stage of Elastic-Plastic Spherical Contact Fretting

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
A. Ovcharenko ◽  
I. Etsion
Keyword(s):  
Energy Dissipation ◽  
Friction Force ◽  
Contact Area ◽  
Early Stage ◽  
Static Friction ◽  
Relative Displacement ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Direct Measurements ◽  
Elastic Perfectly Plastic

The contact area, friction force, and relative displacement evolution at the very early stage of fretting are investigated experimentally. Copper and steel spheres of various diameters are loaded against a hard sapphire flat by a range of normal loads deep into the elastic-plastic regime of deformation. A reciprocating tangential loading is then applied with a maximum loading below the static friction to avoid gross slip. Real-time and in situ direct measurements of the contact area, along with accurate measurements of the friction force and relative displacement, reveal substantial junction growth and energy dissipation mainly in the first loading cycle. The so-called “slip amplitude” is found to be attributed to residual tangential plastic deformation rather than to interfacial slip. Elastic shake-down is observed for the 2.5% hardening steel spheres while plastic shake-down is observed in the case of the elastic perfectly-plastic copper spheres.

A General Autofrettage Model of a Thick-Walled Cylinder Based on Tensile-Compressive Stress-Strain Curve of a Material

2005 ◽  
Vol 40 (6) ◽  
pp. 599-607 ◽  
Author(s):  
X. P Huang
Keyword(s):  
Strain Hardening ◽  
Compressive Stress ◽  
Bauschinger Effect ◽  
Strain Curve ◽  
Accurate Prediction ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Perfectly Plastic ◽  
Hardening Models ◽  
Elastic Perfectly Plastic

The basic autofrettage theory assumes elastic-perfectly plastic behaviour. Because of the Bauschinger effect and strain-hardening, most materials do not display elastic-perfectly plastic properties and consequently various autofrettage models are based on different simplified material strain-hardening models, which assume linear strain-hardening or power strain-hardening or a combination of these strain-hardening models. This approach gives a more accurate prediction than the elastic-perfectly plastic model and is suitable for different strain-hardening materials. In this paper, a general autofrettage model that incorporates the material strain-hardening relationship and the Bauschinger effect, based upon the actual tensile-compressive stress-strain curve of a material is proposed. The model incorporates the von Mises yield criterion, an incompressible material, and the plane strain condition. Analytic expressions for the residual stress distribution have been derived. Experimental results show that the present model has a stronger curve-fitting ability and gives a more accurate prediction. Several other models are shown to be special cases of the general model presented in this paper. The parameters needed in the model are determined by fitting the actual tensile-compressive curve of the material, and the maximum strain of this curve should closely represent the maximum equivalent strain at the inner surface of the cylinder under maximum autofrettage pressure.

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