The Incremental Strain Growth of Elastic-Plastic Bodies Subjected to High Levels of Cyclic Thermal Loading

1984 ◽  
Vol 51 (3) ◽  
pp. 470-474 ◽  
Author(s):  
A. R. S. Ponter ◽  
A. C. F. Cocks
Keyword(s):  
Mechanical Loading ◽  
Yield Surface ◽  
Thermal Loading ◽  
Local Curvature ◽  
Cyclic Thermal Loading ◽  
Elastic Plastic ◽  
Plastic Shakedown ◽  
Incremental Strain

A linearized method of analysis proposed in an accompanying paper [1] is used to obtain the ratchet rate for two types of thermal loading problems where parts of the structure experience reversed plastic straining. For structures that can shakedown plasticially it is found that for a given increment of load beyond the plastic shakedown boundary, the rate of ratchet increases with increasing level of thermal loading. When a structure is unable to shakedown plastically it ratchets at low mechanical loading as the result of a localized mechanism that involves some reversed plasticity. It is shown that the ratchet rate in such situations can be substantial but its value is very dependent on the local curvature of the yield and not the accuracy of the yield surface itself.

Computation of Ratchet Limits for Structures Subjected to Cyclic Loading and Temperature

2002 ◽  
Author(s):  
A. R. S. Ponter ◽  
H. Chen ◽  
M. Habibullah
Keyword(s):  
Finite Element ◽  
Cyclic Loading ◽  
Mechanical Loading ◽  
Limit Theorems ◽  
Thermal Loading ◽  
Loading History ◽  
Cyclic Thermal Loading ◽  
Elastic Plastic ◽  
Plastic Structure ◽  
Shakedown Limit

The paper discusses methods of evaluating the ratchet limit for an elastic/plastic structure subjected to cyclic thermal and mechanical loading. A recently developed minimization theorems by Ponter and Chen [2] provides a generalization of the shakedown limit theorems for histories of load in excess of shakedown. This allows the development of programming methods that locate the ratchet boundary in excess of shakedown. Examples of applications are provided including the performance of a cracked body subjected to cyclic thermal loading. Finally, the theory is used to discuss Kalnins’ [4] proposal that short cut finite element solutions may be used to assess whether a particular loading history lies within a ratchet limit.

Approximate method for the analysis of components undergoing ratchetting and failure

1998 ◽  
Vol 33 (1) ◽  
pp. 55-65 ◽  
Author(s):  
J Lin ◽  
F P E Dunne ◽  
D R Hayhurst
Keyword(s):  
Approximate Method ◽  
Mechanical Loading ◽  
Thermal Loading ◽  
Cyclic Plasticity ◽  
Processing Unit ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Cyclic Thermal Loading ◽  
Central Processing ◽  
Practical Design

An approximate method has been presented for the design analysis of engineering components subjected to combined cyclic thermal and mechanical loading. The method is based on the discretization of components using multibar modelling which enables the effects of stress redistribution to be included as creep and cyclic plasticity damage evolves. Cycle jumping methods have also been presented which extend previous methods to handle problems in which incremental plastic straining (ratchetting) occurs. Cycle jumping leads to considerable reductions in computer CPU (central processing unit) resources, and this has been shown for a range of loading conditions. The cycle jumping technique has been utilized to analyse the ratchetting behaviour of a multibar structure selected to model geometrical and thermomechanical effects typically encountered in practical design situations. The method has been used to predict the behaviour of a component when subjected to cyclic thermal loading, and the results compared with those obtained from detailed finite element analysis. The method is also used to analyse the same component when subjected to constant mechanical loading, in addition to cyclic thermal loading leading to ratchetting. The important features of the two analyses are then compared. In this way, the multibar modelling is shown to enable the computationally efficient analysis of engineering components.

scholarly journals Shakedown of a Thick Cylinder With a Radial Crosshole

2006 ◽  
Author(s):  
Duncan Camilleri ◽  
Donald Mackenzie ◽  
Robert Hamilton
Keyword(s):  
Thermal Loading ◽  
Constant Pressure ◽  
Element Analysis ◽  
Cyclic Thermal Loading ◽  
Interaction Diagram ◽  
Thin Cylinder ◽  
Structural Discontinuity ◽  
Thick Cylinder ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The shakedown behaviour of a thin cylinder subject to constant pressure and cyclic thermal loading is described by the well known Bree diagram. In this paper, the shakedown and ratchetting behaviour of a thin cylinder, a thick cylinder and a thick cylinder with a radial crosshole is investigated by inelastic finite element analysis. Load interaction diagrams identifying regions of elastic shakedown, plastic shakedown and ratchetting are presented. The interaction diagrams for the plain cylinders are shown to be similar to the Bree Diagram. Incorporating the radial crossbore in the thick cylinder significantly reduces the plastic shakedown boundary on the interaction diagram but does not significantly affect the ratchet boundary. The radial crosshole can therefore be regarded as a local structural discontinuity and neglected when determining the maximum shakedown or (primary plus secondary stress) load in Design by Analysis.

An FEA Investigation Into Ratchetting Induced Purely by Cyclic Thermal Loading

2014 ◽  
Author(s):  
Conor S. Campbell ◽  
Donald Mackenzie
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Thermal Loading ◽  
Plastic Material ◽  
Lead Author ◽  
Element Analysis ◽  
Linear Temperature ◽  
Cyclic Thermal Loading ◽  
Elastic Plastic ◽  
Model Structures

A detailed finite element investigation of the cyclic elastic-plastic response of three model structures subject to thermal and mechanical loading is presented within the context of ASME B&PV Code Section VIII Division 2 design requirements. The model structures are a thin tube subject to constant internal pressure and a cyclic through-thickness linear temperature gradient (the Bree problem), a three bar system subject to cyclic thermal loading only and an intermediate thickness tube subject to internal pressure and an axially moving cyclic temperature wave. Incremental elastic-plastic finite element analysis assuming an elastic-perfectly-plastic material model and small deformation theory is performed for each model structure and ratchet and shakedown boundaries determined by application of a bisection method. Results are compared with ASME VIII ratcheting assessment procedures. The results show that in the Bree problem ratcheting does not occur under thermal loading alone, as expected, however for the two other sample structures it is shown that ratchetting can occur under thermal loading for structures subject to specific deformation constraints. The lead author is an MS level student at the University of Strathclyde.

A Nonlinear Multi-Domain Thermomechanical Stress Analysis Method for Surface-Mount Solder Joints—Part II: Viscoplastic Analysis

1997 ◽  
Vol 119 (3) ◽  
pp. 177-182 ◽  
Author(s):  
S. Ling ◽  
A. Dasgupta
Keyword(s):  
Solder Joint ◽  
Potential Energy ◽  
Stress Analysis ◽  
Thermal Loading ◽  
Solder Joints ◽  
Stress And Strain ◽  
Thermomechanical Stress ◽  
Cyclic Thermal Loading ◽  
Surface Mount ◽  
Elastic Plastic

This is part II of a two-part paper presented by the authors for thermomechanical stress analysis of surface mount interconnects. A generalized multi-domain Rayleigh Ritz (MDRR) stress analysis technique has been developed to obtain the stress and strain fields in surface-mount solder joints under cyclic thermal loading conditions. The methodology was first proposed in Part I by the authors and results were presented for elastic-plastic loading (Ling et al., 1996). This paper extends the analysis for viscoplastic material properties. The solder joint domain is discretized selectively into colonies of nested sub-domains at locations where high stress concentrations are expected. Potential energy stored in the solder domain and in the attached lead and Printed Wiring Board (PWB) is calculated based on an assumed displacement field. Minimization of this potential energy provides a unique solution for the displacement field, consequently, stress and strain distribution. The MDRR technique was demonstrated to provide reasonable accuracy for elastic deformation (Ling and Dasgupta, 1995) and for time-independent elastic-plastic deformation (Ling and Dasgupta, 1996) for solder joints under cyclic thermal loading conditions. A piecewise linear incremental loading technique is used to solve the nonlinear elastic-plastic problem. The focus in the current paper is primarily on time-dependent viscoplastic deformation of the solder joints. Full field elastic, plastic, and viscoplastic analyses are performed, and the stress, strain hysteresis loops are obtained. Results are presented for a J-lead solder joint as an illustrative example.

scholarly journals Shakedown of a Thick Cylinder With a Radial Crosshole

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Duncan Camilleri ◽  
Donald Mackenzie ◽  
Robert Hamilton
Keyword(s):  
Thermal Loading ◽  
Constant Pressure ◽  
Element Analysis ◽  
Cyclic Thermal Loading ◽  
Interaction Diagram ◽  
Thin Cylinder ◽  
Structural Discontinuity ◽  
Thick Cylinder ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The shakedown behavior of a thin cylinder subject to constant pressure and cyclic thermal loading is described by the well known Bree diagram. In this paper, the shakedown and ratchetting behavior of a thin cylinder, a thick cylinder, and a thick cylinder with a radial crosshole is investigated by inelastic finite element analysis. Load interaction diagrams identifying regions of elastic shakedown, plastic shakedown, and ratchetting are presented. The interaction diagrams for the plain cylinders are shown to be similar to the Bree diagram. Incorporating a radial crossbore, Rc∕Ri=0.1 or less, in the thick cylinder significantly reduces the plastic shakedown boundary on the interaction diagram but does not significantly affect the ratchet boundary. The radial crosshole, for the geometry considered in this study, can be regarded as a local structural discontinuity and neglected when determining the maximum shakedown or (primary plus secondary stress) load in design by analysis. This may not be apparent to the design engineer, and no obvious guidance, for determining whether a crosshole is a local or global discontinuity, is given in the codes.

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