Representing the Effect of Crystallographic Texture on the Anisotropic Performance Behavior of Rolled Aluminum Plate

1999 ◽  
Vol 122 (1) ◽  
pp. 10-17 ◽  
Author(s):  
M. P. Miller ◽  
N. R. Barton
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Yield Strength ◽  
Upper Bound ◽  
Crystallographic Texture ◽  
Rolling Direction ◽  
Rolled Plate ◽  
Elastic Plastic ◽  
Polycrystal Plasticity ◽  
Rolled Aluminum

Rolled aluminum alloys are known to be anisotropic due to their processing histories. This paper focuses on measuring and modeling monotonic and cyclic strength anisotropies as well as the associated anisotropy of the elastic/elastic-plastic transition of a commercially-available rolled plate product. Monotonic tension tests were conducted on specimens in the rolling plane of 25.4 mm thick AA 7075-T6 plate taken at various angles to the rolling direction (RD). Fully-reversed tension/compression cyclic experiments were also conducted. As expected, we found significant anisotropy in the back-extrapolated yield strength. We also found that the character of the elastic/elastic-plastic transition (knee of the curve) to be dependent on the orientation of the loading axis. The tests performed in RD and TD (transverse direction) had relatively sharp transitions compared to the test data from other orientations. We found the cyclic response of the material to reflect the monotonic anisotropy. The material response reached cyclic stability in 10 cycles or less with very little cyclic hardening or softening observed. For this reason, we focused our modeling effort on predicting the monotonic response. Reckoning that the primary source of anisotropy in the rolled plate is the processing-induced crystallographic texture, we employed the experimentally-measured texture of the undeformed plate material in continuum slip polycrystal plasticity model simulations of the monotonic experiments. Three types of simulations were conducted, upper and lower bound analyses and a finite element calculation that associates an element with each crystal in the aggregate. We found that all three analyses predicted anisotropy of the back-extrapolated yield strength and post-yield behavior with varying degrees of success in correlating the experimental data. In general, the upper and lower bound models predicted larger and smaller differences in the back-extrapolated yield strength, respectively, than was observed in the data. The finite element results resembled those of the upper bound when initially cubic elements were employed. We found that by employing an element shape that was more consistent with typical rolling microstructure, we were able to improve the finite element prediction significantly. The anisotropy of the elastic/elastic-plastic transition predicted by each model was also different in character. The lower bound predicted sharper transitions than the upper bound model, capturing the shape of the knee for the RD and TD data but failing to capture the other orientations. In contrast, the upper bound model predicted relatively long transitions for all orientations. As with the upper bound, the FEM calculation predicted gentle transitions with less transition anisotropy predicted than that of the upper bound. [S0094-4289(00)00201-2]

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Yield Strength ◽  
Stress Component ◽  
Direct Methods ◽  
Theoretical Development ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit

Ensuring sufficient safety against ratchet is a fundamental requirement in pressure vessel design. Determining the ratchet boundary can prove difficult and computationally expensive when using a full elastic–plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with ratchet boundary evaluation. Here, a new approach based on fully implicit finite element methods, similar to conventional elastic–plastic methods, is presented. The method utilizes a two-stage procedure. The first stage determines the cyclic stress state, which can include a varying residual stress component, by repeatedly converging on the solution for the different loads by superposition of elastic stress solutions using a modified elastic–plastic solution. The second stage calculates the constant loads which can be added to the steady cycle while ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength is updated throughout the analysis, thus satisfying Melan's lower bound ratchet theorem. This is achieved utilizing the same elastic plastic model as the first stage, and a modified radial return method. The proposed methods are shown to provide better agreement with upper bound ratchet methods than other lower bound ratchet methods, however limitations in these are identified and discussed.

A Study of Wall Ironing by the Finite Element Technique

1978 ◽  
Vol 100 (1) ◽  
pp. 31-36 ◽  
Author(s):  
E. I. Odell
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Cone Angle ◽  
Reduction Ratio ◽  
Operating Parameters ◽  
Finite Element Technique ◽  
Elastic Plastic ◽  
Maximum Reduction ◽  
Load Displacement ◽  
Element Technique

Wall ironing has been analyzed using an elastic-plastic finite element technique. The effects that the ironing ring semi-cone angle and friction have on the maximum reduction ratio are studied in detail. Stress contours are given for a typical set of operating parameters. Several ram load/displacement curves are provided and compared with upper and lower bound loads.

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Implementation and Comparison

2012 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Hybrid Method ◽  
Direct Methods ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit ◽  
Tangent Moduli

Ensuring sufficient safety against ratcheting is a fundamental requirement of pressure vessel design. However, determining the ratchet boundary using a full elastic plastic finite element analysis can be problematic and a number of direct methods have been proposed to overcome difficulties associated with ratchet boundary evaluation. This paper proposes a new approach, similar to the previously proposed Hybrid method but based on fully implicit elastic-plastic solution strategies. This method utilizes superimposed elastic stresses and modified radial return integration to converge on the residual state throughout, resulting in one Finite Element model suitable for solving the cyclic stresses (stage 1) and performing the augmented limit analysis to determine the ratchet boundary (stage 2). The modified radial return methods for both stages of the analysis are presented, with the corresponding stress update algorithm and resulting consistent tangent moduli. Comparisons with other direct methods for selected benchmark problems are presented. It is shown that the proposed method consistently evaluates a lower bound estimate of the ratchet boundary, which has not been demonstrated for the Hybrid method and is yet to be clearly shown for the UMY and LDYM methods. Limitations in the description of plastic strains and compatibility during the ratchet analysis are identified as being a cause for the differences between the proposed methods and other current upper bound methods.

A Multi-Surface Plasticity Method for Lower Bound Shakedown Load

2019 ◽  
Vol 795 ◽  
pp. 458-465
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Hao Feng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Finite Number ◽  
Upper Bound ◽  
Direct Method ◽  
Extreme Points ◽  
Residual Stress Field ◽  
Periodic Load ◽  
Surface Plasticity ◽  
Elastic Shakedown

A new direct method for calculation of lower bound shakedown limits based on Melan’s theorem and a novel, non-smooth multi-surface plasticity model is proposed and implemented in a Finite Element environment. The load history is defined by a finite number of extreme points defining the load-envelope of a periodic load set. The shakedown problem is stated as a plasticity problem in terms of a finite number of independent yield conditions, solved for a residual stress field that satisfies a piecewise, non-smooth yield surface defined by the intersection of multiple yield surfaces. The implemented Finite Element procedure is applied to two shakedown problems and the results compared with lower and upper bound elastic shakedown solutions given by the Linear Matching Method, LMM. The example analyses show that the proposed Elastic-Shakedown Multi Surface Plasticity (EMSP) method defines robust lower bound shakedown limits between the LMM lower and upper bound limits, close to the LMM upper bound.

Upper and lower bound limit and shakedown loads for hollow tubes with axisymmetric internal projections under axial loading

2001 ◽  
Vol 36 (6) ◽  
pp. 595-604 ◽  
Author(s):  
S. J Hardy ◽  
A. R Gowhari-Anaraki ◽  
M. K Pipelzadeh
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Axial Loading ◽  
Limit Load ◽  
Analysis Procedure ◽  
Elastic Analysis ◽  
Elastic Plastic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Elastic Compensation Method

In this paper, the elastic compensation method proposed by Mackenzie and Boyle is used to estimate the upper and lower bound limit (collapse) loads and the upper and lower bound shakedown loads for hollow tubes with axisymmetric internal projections subjected to axial loading. The method is based on an iterative elastic analysis procedure and the application of lower and upper bound limit load theorems. Four different geometries with a range of stress concentration factors (from low to high) are considered. Elastic-plastic finite element predictions for collapse and shakedown pressure are found to be within these upper and lower bound estimates. The method is particularly useful because it is founded on an iterative elastic approach and does not require extensive and complex elastic-plastic finite element computations.

A Simple Upper-Bound Method for Calculating Approximate Shakedown Loads

1998 ◽  
Vol 120 (2) ◽  
pp. 195-199 ◽  
Author(s):  
R. Hamilton ◽  
J. T. Boyle ◽  
J. Shi ◽  
D. Mackenzie
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Spherical Shell ◽  
Upper Bound ◽  
Pressure Vessel ◽  
Simple Approach ◽  
Finite Element Analyses ◽  
Axisymmetric Nozzle ◽  
Upper Bound Method

A simple approach for calculating upper-bound shakedown loads is described. The method is based on a series of iterative elastic finite element analyses (the elastic compensation procedure) applied to Koiter’s upper-bound shakedown theorem. The method is demonstrated for a typical pressure vessel application; an axisymmetric nozzle in a spherical shell. Several geometrical configurations are investigated. The calculated upper-bound shakedown loads are compared with lower-bound results obtained by the authors, simple shakedown criteria, and various results given in the literature.

Analysis of the spherical indentation cycle for elastic–perfectly plastic solids

2004 ◽  
Vol 19 (12) ◽  
pp. 3641-3653 ◽  
Author(s):  
L. Kogut ◽  
K. Komvopoulos
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Elastic Modulus ◽  
Yield Strength ◽  
Material Properties ◽  
Deformation Behavior ◽  
Plastic Material ◽  
Elastic Plastic ◽  
Loading And Unloading ◽  
Elastic Plastic Material

A finite element analysis of frictionless indentation of an elastic–plastic half-space by a rigid sphere is presented and the deformation behavior during loading and unloading is examined in terms of the interference and elastic–plastic material properties. The analysis yields dimensionless constitutive relationships for the normal load, contact area, and mean contact pressure during loading for a wide range of material properties and interference ranging from the inception of yielding to the initiation of fully plastic deformation. The boundaries between elastic, elastic–plastic, and fully plastic deformation regimes are determined in terms of the interference, mean contact pressure, and reduced elastic modulus-to-yield strength ratio. Relationships for the hardness and associated interference versus elastic–plastic material properties and truncated contact radius are introduced, and the shape of the plastic zone and maximum equivalent plastic strain are interpreted in light of finite element results. The unloading response is examined to evaluate the validity of basic assumptions in traditional indentation approaches used to measure the hardness and reduced elastic modulus of materials. It is shown that knowledge of the deformation behavior under both loading and unloading conditions is essential for accurate determination of the true hardness and reduced elastic modulus. An iterative approach for determining the reduced elastic modulus, yield strength, and hardness from indentation experiments and finite element solutions is proposed as an alternative to the traditional method.

Shakedown Analysis of Axisymmetric Nozzles Under Primary and Secondary Cyclic Loads

2009 ◽  
Author(s):  
Dan Vlaicu
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Stress Field ◽  
Material Properties ◽  
Cyclic Load ◽  
Elastic Stress ◽  
Nonlinear Material ◽  
Cyclic Loads ◽  
Shakedown Analysis ◽  
Elastic Plastic

In this paper, the finite element method is used to develop the lower bound limit for the elastic shakedown analysis of axisymmetric nozzles under periodic loading conditions. The Nonlinear Superposition Method is employed to calculate the lower bound shakedown loads by quoting Melan’s theorem in a nonlinear finite element analysis. The calculation is divided into two separate iterations which are blended with a technique that matches the elastic-plastic part of the analysis with the linear part. In the first part of the calculation, the cyclic load is applied as a static load to generate an elastic stress field in the structure. The same cyclic load is subsequently combined with the constant fraction of the load in the second part of the calculation, and the total load is applied in an elastic-plastic analysis that exceeds the yield limit. For each solution increment, the residual stress is generated from the superposition of the elastic stress field scaled through the applied cyclic load and the shakedown stress field calculated from the nonlinear analysis. The results obtained from the lower bound method are compared with the full cyclic loading analyses based on nonlinear material properties, and this paper discusses the choice of the global shakedown in terms of the radial strain, and the local through thickness shakedown defined by the hoop strain. Furthermore, this paper presents the development of a generic model that emulates the behavior of the finite element model under cyclic loads in a simplified form, with the statistical representation based on a sampling of base-model data for a variety of test cases. The probabilistic method takes variations of the geometrical dimensions, nonlinear material properties, and pressure load as the input parameters, whereas the response variable is defined in terms of the lower bound of the shakedown loads.

Influence of Crystallographic Texture on Mechanical Properties in Cold Rolled 7XXX Series Al Alloys Used in Space Applications

2012 ◽  
Vol 710 ◽  
pp. 539-544 ◽  
Author(s):  
P. Ramesh Narayanan ◽  
Satyam Suwas ◽  
K. Sreekumar ◽  
Parameshwar Prasad Sinha ◽  
Srinivasa Ranganathan
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Ultimate Tensile Strength ◽  
Yield Strength ◽  
Crystallographic Texture ◽  
Shear Banding ◽  
Rolling Direction ◽  
The Other ◽  
Space Applications ◽  
Plastic Strain Ratio

This paper covers the influence of crystallographic texture on the mechanical properties in two of the most important high strength Al-Zn-Mg family of aluminium alloys, viz., AA7075 and AFNOR7020 alloys, used in the Aerospace industry. AFNOR7020 Alloy developed a stronger texture compared to the other two alloys. S component of texture is stronger in AA7075 alloy whereas the Bs component is stronger in AFNOR7020 alloy. This is attributed to the shear banding which was found absent in the other alloy. The starting material, AA7075 in T7352 condition and AFNOR7020 in T652 condition show some degree of anisotropy of mechanical properties with regard to yield strength and ultimate tensile strength. Higher degree of deformation leads to more pronounced anisotropy in mechanical properties with regard to yield strength and ultimate tensile strength, with a maxima along the transverse direction. For the alloys, experimentally measured Plastic Strain Ratio, r value, which is a measure of the texture present in the material in the deformation conditions, agree well with the computed values with a maximum at 45oorientation to the rolling direction.

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