Abaqus Finite Element Analysis of Cyclic Loading on a ：在循環(huán)加載ABAQUS有限元分析

1、Accuracy of Fully Elastic vs. Elastic-Plastic Finite Element AnalysisBy: Nicholas SzwajaMay 25, 2012Masters of Engineering Project ProposalSubmitted to the Graduate Faculty of Rensselaer Polytechnic Institute to Fulfill the Requirement for the Degree of Masters of Engineering, Mechanical Engineering

2、AbstractThe objective of this master of engineering final project is to investigate and analyze the accuracy of Finite Element Analysis (FEA) when it is used to compare fully elastic and elastic-plastic deformation in High Strength Steel (HSS). HSS, like many metals, displays a linear relationship b

3、etween stress and strain until a yield point is reached 1. At the yield point, if force is still applied, the material will plastically deform and will not regenerate to its original shape 2. In the plastic range, the relationship between stress over strain is no longer linear 2; as a result, as mor

4、e force is applied to the material, the variable of strain increases in larger increments with respect to stress until the material fractures 2.Elastic and/or plastic material properties can be used when performing FEA. Plasticity is primarily analyzed in plastics and certain composites because of t

5、heir low modulus of elasticity 3 or forgings. In HSS, FEA analysis can be performed using fully elastic material properties, however this may not be the best analysis to perform. When using HSS to design a component, once the material goes beyond its yield point, permanent deformation will occur whi

6、ch, for a structural design typically results in failure of the component. To capture plastic deformation in FEA, tabular/experimental data of yield stress and strain in the plastic range is required to ensure the material can be deformed past the yield point and permanent deformation can be accurat

7、ely analyzed. The tabular data is from Data Point Labs, Ithaca NY. This study will perform a comparison study to determine the accuracy of fully elastic versus elastic-plastic analysis in FEA of HSS in tension and compression. This analysis will include a FEA tensile/compression test analysis of a t

8、est specimen from ASME E8 using fully elastic material properties and comparing the results to elastic-plastic deformation of HSS. Introduction and BackgroundTensile test are performed to determine / validate the load capacity of a material 4. The tensile test specimen that will be modeled in FEA wi

9、ll be specimen 1 from ASME E8 also depicted in Figure 1. Specimen 1 is a standard test specimen that is threaded into an apparatus that will continuously supply a tensile/compressive load until the specimen fails. The material of the specimen will be made out of High Strength Steel (HSS) due to the

10、high loads it can withstand and its use in various structural components. The data collected can be used to accurately design a system to ensure failure, deflection, or permanent deformation does not affect the original intent of the design. Figure 2 from Reference 5 are predicted results of a tensi

11、le pull test of various metals. From the results of the load test, the variables of stress, strain, modulus of elasticity, yield point, ultimate strength, necking, and fracture points can be determined. The graph depicts both the elastic and plastic range. The FEA analysis of this project will look

12、at FEA results of just the elastic range with a high load and the elastic into plastic range with a high load and analyze the accuracy. Also the elastic-plastic model will be reversely loaded in FEA to analyze the stress strain in a compressive load. Figure 1: Specimen 1 geometry used in FEA Abaqus

13、from ASME E8Figure 2: Stress / Strain Curve various metals. Reference5The fully elastic range is from the origin (0,0) to the yield point. This is a linear relationship 1. When designing components that have to withstand high loads, the design goal is to stay within the elastic range to avoid perman

14、ent deformation. Beyond yield point, the plastic range is achieved 2. The plastic range is nonlinear and once the load is released, the material will not regenerate to its original shape 6. Although plasticity in metals is not considered ideal for a majority of structural and mechanical designs, the

15、re are cases when understanding of the plastic range plays a pertinent roll in engineering. This includes but is not limited to forging, fracture mechanics, plastics, and selected composites. By taking the elastic-plastic model and reversely loading it into compression, the analysis will depict what

16、 takes place in the stress strain during reverse loading of the test specimen.Fully Elastic Deformation in FEAFully elastic deformation is defined as reversible alteration of the form or dimensions of a solid body under stress or strain 7. When a material is placed under a load, the part will be str

17、essed but will maintain the ability to return to its original shape. Fully elastic deformation is typically governed by Hookes Law 4 which states: = Ewhere: = StressE = Modulus of Elasticity = StrainHookes Law is a linear relationship that relates stress to strain by using the modulus of elasticity

18、of the material 8. Fully elastic analysis only pertains to stress and strain up to the yield point. In FEA Abaqus, only the modulus of elasticity is needed to perform this analysis. In this study hand calculations using Hookes law and other finite element methods will be used to validate the fully e

19、lastic FEA results to ensure that FEA is producing accurate analysis in the fully elastic range.Elastic-Plastic Deformation in FEAPlastic deformation is defined as permanent change in shape or size of a solid body without fracture resulting from the application of sustained stress beyond the elastic

20、 limit 9. Elastic-plastic analysis uses the modulus of elasticity from the elastic material properties but FEA Abaqus requires plastic range yield stress and strains of the material in the plastic range. An important point to consider, is that if the plasticity data has not been entered into FEA Aba

21、qus, the stress/strain relationship will continue to be erroneously linear. This will not provide an accurate result of stress in the plastic range. The concern with mathematically analyzing plastic deformation is that the existing theories are constructed largely on the basis of mathematical consid

22、erations and involve a number of arbitrary assumptions of uncertain validity 9. More experimental data needs to be obtained to validate the numerical solutions. FEA is a method of using the experimental data from plastic deformation (yield stress and strain) and analyzing the deformation in the plas

23、tic range 9. As a result, this reduces the number of assumptions and leads to a more accurate result. Significant work has been done to provide a more analytical method for calculating stress in the plastic range 9 11 and hand calculations will be provided to validate that the stress/strain relation

24、ship provided by FEA Abaqus. Problem Description and MethodologyA tensile test validates material and mechanical properties in the fully elastic and elastic-plastic range of any material. An important point to note is that the sample provided to do the test may not have the same mechanical propertie

25、s as the material in the final manufactured component of the design; however this test is performed solely to represent a general range. The tensile test is an approximation and just like FEA, can not always be 100% accurate. The goal of this project is to use FEA Abaqus to perform a comparison betw

26、een fully elastic material properties and elastic plastic material properties. Data Point Labs has provided High Strength Steel (HSS) tensile test results at different strain rates to compare for accuracy of the FEA and hand calculations. The first analysis will involve a tensile test sample, modeli

27、ng it in Abaqus, and putting a large tensile load on the sample. This first analysis will only focus on fully elastic material properties up to the yield point and then analyze how FEA performs with large loads past the elastic range. These results will be confirmed with hand calculations and the Da

28、ta Point Lab results to verify the accuracy of FEA. The second analysis will once again utilize the same tensile test sample, however manual input of plastic deformation stress/strain values will be provided. Hand calculations will be performed to calculate the theoretical strength of the HSS and co

29、mpared to the FEA results and the DATA Point Labs results to come to a conclusion on accuracy. Once the analysis is complete, a comprehensive comparison will be performed to determine the accuracy of fully elastic versus elastic-plastic deformation in FEA when compared to actual test results from Da

30、ta Point Labs. Data Points Labs performed multiple tensile tests at different strain rates and the FEA Abaqus results and the theoretical strength hand calculations will be compared to determine the accuracy of FEA to actual test data.The elastic-plastic FEA analysis, reverse loading will be analyze

31、d. With the elastic-plastic data input into the material properties in FEA Abaqus, the test specimen will be reversely loaded to analyze how the test specimen reacts to reverse loading.Resources RequiredThe following resources are required to complete the project: Abaqus Finite Element Analysis (FEA

32、): Version 6.10-EF1 Microsoft Office (Word, Excel, power point) Math CadThe Abaqus FEA software is required to complete this project and will be the main tool used in the analysis and to evaluate the fully elastic and elastic-plastic conditions. Abaqus is an ideal program to analyze the tensile test

33、 because it is a program used to analyze structural and mechanical problems. Math Cad will be the computer software used to derive equations and verify the FEA solution performed in Abaqus. The Microsoft Office tools (Word and Power Point) will be used to write the report and develop presentations.E

34、xpected OutcomeThe expected outcome of this master of engineering project is to apply engineering principles and resources to understand how fully elastic and elastic-plastic analysis in FEA Abaqus relates. The expected outcome is that at lower stress levels, the fully elastic and elastic-plastic st

35、rains will be similar until the yield point is reached. There is no expected discrepancy in the stress/strain relationship 11. Once the applied load is extended past the yield point it is expected that the fully elastic model will show inaccurate results because the stress/strain will continue to be

36、 linear. On the other hand, the elastic-plastic analysis will maintain its accuracy based on the additional material property values provided for the plastic range. The FEA will be compared to the Data Point Lab tensile test results and the expected outcome will be fairly accurate based on the strai

37、n rates. As the strain rates increase there are some expected differences in the higher stresses due to variations in the modulus of elasticity 12. Tentative Work Schedule Research fully elastic and elastic-plastic material deformation and relationship of high strength steel (HSS) Develop Abaqus mod

38、el - Create model, apply correct material properties (fully elastic and elastic-plastic), perform mesh density study, obtain result (von mises, stress/strain curves, stress concentrations) Derive equations in Math Cad to verify Abaqus results and obtain tensile test results for comparison Compile da

39、ta Abaqus and Math Cad solutions Come to conclusions on results Stay in contact with RPI Faculty by providing regular updates, follow online schedule (class website), and regular ask questions/concerns that will come up Write and submit final reportThe schedule below takes into account all various activities to complete the project within 15 weeks. The schedule includes milestones, important tasks, and a roadmap to completion. Referen