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Simulation of Non-Linear Analysis - 2006 ANSYS Conference-LR's Paper

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   2006 India Users Conference   Simulation of Non-Linear Analysis in  ANSYS   L Ramanan Principal Engineer, Advanced Mech. Engineering GE Healthcare Technologies, GTO India. ramanan.l@ge.com Abstract: Simulation of many real life problems is highly complex in nature and involves non-linear behavior to be accurately modeled.  ANSYS   non-linear capabilities over the years have evolved according to the emerging analysis needs, maturity of analysis methods and increased computing power. GE has a global understanding with  ANSYS   and uses the code for some of its non-linear needs. This paper aim at explaining the capability and settings needed in performing non-linear analysis in  ANSYS   through a simplified example problem. Introduction:  Numerical simulation plays a very important and an indispensable role in the manufacturing process [1], reducing the cycle time in design [2] while improving the quality and performance and simulation of a  behavior like crash [3]. In the recent times analysts and designers have begun to use numerical simulation alone as an acceptable means of validation in designing the components for six-sigma quality. In many disciplines, virtual prototyping  – employing numerical simulation tools based on finite element methods-has replaced traditional build and break prototyping. Leading world standards [American Association of Rail Roads – AAR] for locomotive designs have standard like AAR-S-660-83 [4], AAR-S-5506 [5] for designing some of the critical components like rail wheel, fuel tank etc. Finite element method has been an accepted as an industry standard [6] in satisfying the regulatory needs of some of the locomotive’s critical component. All of the above examples quoted are highly non-linear involving all the three different type of non-linearity namely geometric, material and boundary. For simulating the non-linear analysis in a reliable manner, the following components are necessary in the FE analysis tool [7] 1) Element Technologies for consistent large-deformation treatment 2) Constitutive models for a variety of metals and nonmetals 3) Contact Interaction and Assembly Analysis 4) Solution of large-scale problems (where multiple nonlinearities interact in a complex manner) and 5) Infrastructure In this paper attempt has been made to explain the generic capabilities available in ANSYS for simulating such a large deflection, large strain problems through a very simplified problem. The actual problem in which  ANSYS   has been used was to predict the effects of large deflection due to the impact of medical equipments in the hospital environment in one of our medical devices. Simulation studies have been later corroborated with experimental validation. Product concept developed to the medical device of MR patient table handling system has been filed for patenting in US [8]. In explaining the non-linear problem the material considered in this paper is steel and hence the paper does not address the capability of  ANSYS   in simulating “Hyper Elastic” material model. It is impossible given the scope of the paper to address every available analysis feature of  ANSYS  ; rather attempt has been made to highlight the key features of interest to most analyst and design engineers.   2006 India Users Conference   Nonlinear Material Capability: Material behavior is a very complex science. A wide variety of approaches are used to best match the computer simulation of a material to the response actually observed. The nonlinear behavior comes into  picture when the component is loaded beyond its proportional limit. It is a known fact that the stress is  proportional to strain upto limit of proportionality [Figure 1] and is governed by Hooke’s law. For non-linear behavior, stress is no longer proportional to strain. The various types of non-linearity and their dependency is explained extensively in reference [9] by Ray and Guoyo. It is not within the scope of this  paper to address the entire non-linear behavior. The scope of the work is restricted with nonlinear, inelastic and rate-independent materials, since most of the metals fall into this category at lower temperature (temperature below half of the metal’s melting point temperature). Plastic Behavior and Modeling in ANSYS: When a material is subjected to an external load of such magnitude that deformation continues with no apparent further increase in load, the material is said to have become plastic. Once in this region, the material will not return back to its srcinal shape when the load is removed and hence the materiel / component has experienced permanent deformation. At the time of application of external load in plastic region, the component experiences the total strain, which comprises of plastic strain and a small amount of recoverable elastic strain. Figure 1 explains the typical stress strain curve of low carbon steel (mild steel) tensile test specimen. In general, the stress strain data, which are measured through tensile test, and the data available in the material handbook are the “Engineering Stress and Engineering Strain”. Figure 1 – Stress - Strain Curve of Low Carbon Steel But most of the non-linear FE analysis tools require the data to be in the form of “True Stress to True Strain” for FE analysis. ANSYS also from its version 5.0 required that the values of stress and strain be inputted as true stress and true strain. The true stress to true strain curve of the above low carbon steel will  be represented as seen in Figure 2.   2006 India Users Conference  Figure 2 – True Stress – True Strain Curve of Low Carbon Steel Generally, the material data available for most of the metals from the data book are yield strength, ultimate tensile strength (UTS) and elongation %. Typical data of ASTM-A-36 material model is shown in Table-1. The data of engineering stress and strain of typical ASTM-A-36 material model is shown in Table 1. Material Young’s Modulus (E) in psi Poisson’s Ratio Yield strength in  psi Ultimate Tensile Strength Elongation  percentage ASTM-A-36 2.9 E7 0.29 36000 58000 23 Table-1 Engineering Stress Strain data of ASTM-A-36 Material The engineering data and need to be converted to true data for use in FE analysis and can be converted using the following equations. For low values of strain, there would not be any difference between true data and engineering data [9]. In general, most of the non-linear FE analysis tool available in the market uses the true stress to true strain relation ship while modeling non-linear plasticity model. Most of them uses the true plastic strain and true stress data, hence the first data point in those codes will follow the following format for the example material shown in Table-1 0.0, 36000 (True plastic strain at yield, True yield stress) … (1) 0.2050, 71340 (True plastic strain at UTS, True ultimate stress) … (2) If the data available in between the yield and UTS, it can be converted to true format and used between the data lines (1) & (2) above.   2006 India Users Conference  Since  ANSYS   uses the true total strain and true stress, the first data point cannot be zero. Hence the data to  be used in  ANSYS would be as follows 0.001241, 36000 (True total strain at yield, True yield stress) … (3) 0.2070, 71340 (True total strain at UTS, True ultimate stress) … (4) The true total strain in the data line (3) for  ANSYS   has been calculated using the following relationship  ANSYS   considers that there is no difference between the point A and B of Figure 1, and hence calculates the total strain using the relationship between yield stress and Young’s modulus. The data lines (3) and (4) are the inputs in multilinear material data table of  ANSYS   and is shown in Figure 3. Figure 3. ASTM-A-36 Material Data in ANSYS for Modeling Material Plasticity-Multi Linear Option Handling of Convergence while Modeling Plastic Behavior: When the material enters from the elasto-plastic to perfectly plastic region [Figure 2] in the FE analysis, it could lead to convergence issues. Generally to circumvent this, it is the practice in the Industry to have a  point above the UTS by extrapolating the data. However, care has to be taken while interpreting the results.  ANSYS   has the option of modeling the plasticity data through Bi-Linear material model, which would avoid convergence issues due to material model in plasticity analysis. The material data line for Bi-Linear modeling in  ANSYS   of the ASTM-A-36 material model would be as follows. 36000 (Yield Strength of the material) … (4) 171754.33 (Tangent Modulus) … (5) The tangent modulus / slope of the curve has been calculated using the true stress and true strain data of the ASTM-A-36 material model and is as follows.
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