DETERMINATION OF MATERIAL PROPERTIES AND VALIDATION OF TENSILE TESTING BY FINITE ELEMENT METHODS

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Organized by C.O.E.T, Akola & IWWA, Amravati Center. Available Online at www.ijpret.com257

INTERNATIONAL JOURNAL OF PURE AND

APPLIED RESEARCH IN ENGINEERING AND

TECHNOLOGY

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SPECIAL ISSUE FOR

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"SUSTAINABLE TECHNOLOGIES IN

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“DETERMINATION OF MATERIAL PROPERTIES & VALIDATION OF TENSILE

TESTING BY FINITE ELEMENT METHODS”

DR. DHARMENDRA C. KOTHARI, PROF. PRASHANT V. THORAT

Department of Chemical Engineering & Polymer & Technology, Shri. Shivaji Education Society AMRAVATI’s COLLEGE OF ENGINEERING & TECHNOLOGY, BABHULGAON, AKOLA, 444104, Maharashtra.

Accepted Date: 13/03/2015; Published Date: 01/04/2015

Abstract – The growth in use of finite element methods is directly attributable to the rapid advances in computing technology in recent years. Today there are a number of large software companies developing and marketing finite element and associated modelling software. As a result, there exist commercial finite element packages capable of solving the most sophisticated problem, not just in structural or stress analysis, but for a wide range of phenomena such as steady and dynamic temperature distributions, fluid flow, and manufacturing processes such as forming processes. In many of these analyses re-meshing is essential due to the irregular behaviour of pasty materials. The nature of the plastic deformation that occurs in soft-solids was examined under uniaxial tension by measuring the load history of a deforming specimen at a constant cross-head speed. These preliminary load and displacement data were converted into stress, strain and strain rate relationships in order to obtain the Young’s modulus, the yield stress and the engineering strain. In order to interpret tensile measurements in terms of basic material properties such as elastic modulus and yield stress, it is necessary to have a mechanics model of the tension process. The model was be able to provide quantitative material parameters from data obtained at different strain-rates.

Keywords-Tensile Test, Soft-Solids, Activation Energy & Finite Elements Analysis (FEA).

Corresponding Author: DR. DHARMENDRA C. KOTHARI Co Author: PROF. PRASHANT V. THORAT

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How to Cite This Article:

Dharmendra C. Kothari, IJPRET, 2015; Volume 3 (8): 257-265

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INTRODUCTION

The material properties of interest in this research are the ultimate strength, the yield strength, the elastic moduli, the strain-to-failure, and the Poisson’s ratio. In past the tensile test has been used to evaluate the strength of all kinds of materials ranging from soft solids, to metals and alloys. In these tests soft solid samples are usually pulled to failure in a relatively short time at a constant extension rate. The force displacement data obtained may be converted to engineering stress, and a plot of engineering stress against engineering strain could be constructed. The material properties of soft solids which can be obtained from the engineering tensile test are; the modulus of elasticity, yield strength, the ultimate tensile strength, the percent elongation at fracture, and the percent reduction in the area at fracture, (Hertzberg, 1996). Necking or localised deformations both occur in materials under uniaxial tensile loading conditions, but their behaviours are different, due to their different mechanisms, Crazes or voids develop and molecules stretch in amorphous solids. Crazes can be regarded as localised, split-shaped, narrow regions of highly deformed material or as an assembly of “micro necks”. Shear bands can be described as localised deformations that develop under the plane strain conditions in which there is no contraction along the length of the specimen, but its thickness decreases. In this study some necking was observed at high speed, while failure was by brittle fracture at low speeds, so materials are considered to be continuum, (Kothari 1999).

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Photograph of INSTRON. Deformation of “Plasticine. Un-deformed specimen.

Figure [1]: - Schematic Diagram of the deformation of Soft-Solids in tensile test uses INSTRON.

METHODOLOGY

The principal device used was a standard universal testing machine (Instron 4301) of Instron Ltd., (High Wycombe, UK), equipped with a 1kN transducer (top load cell) of accuracy  _1N.

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In a representative experiment the load cell output was zeroed with the sample hinged to the flanges, and all the loose distance within the sample was removed by moving the cross-head up. Then the required extension speed was set (normally, in the range 2 mm/min to 500 mm/min), and the top cross-head was moved upwards at the prescribed constant velocity, while the bottom was held at rest. In order to characterise the material properties, the upward motion was continued until the complete rupture of the sample. During the testing the outputs of the load cell and the internal LVDT were recorded, along with the time, using a data acquisition system. The instron was carefully reset at the beginning of every experiment to measure zero load and displacement. Some photographs were taken during the experimentation and are displayed with finite elements validations. Isothermal experimental techniques were followed in which the whole chamber was maintained at constant temperature in an attempt to focus upon and resolve some of the thermo-mechanical phenomena of deformation. The whole experimental environment was raised to the set temperature and allowed to stabilise before the start the testing. The data obtained for the tensile extension provide a means of evaluating the relative values of the two approaches and also extent of their mutual consistency of software and the actual behaviour of materials.

Poisson’s ratio is the absolute value of the ratio of transverse strain to the corresponding axial strain resulting from uniformly distributed axial stress, below the proportional limit of the material. Transverse strain is measured in a direction perpendicular to the applied load and axial strain is measured in the direction parallel to the applied load. Consider the dumbbell shape sample as shown in the Figure [1] subjected to a tensile load. Under the action of this load the dumbbell will increase in length by an amount d giving a longitudinal strain in the bar

of 0 0

0 1 1 L d L L L    

; where the initial length is L0, the final length is L1; and L1 = L0 + d. The bar

will also exhibit, a reduction in dimensions laterally, i.e. its breadth and thickness will both reduce. The associated lateral strains will both be equal, will be of opposite sense to the

longitudinal strain, and will be given by: 0 1 0 0 1 0 2 b b b a a a     

;where the initial width is a0; the

final width is a1,the and initial thickness is b0; final thickness is b1.

The Poisson’s ratio is given by:- = longitudinalstrain

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Poisson’s ratio is dimensionless, with typical values in the range 0.1 to 0.5 and it follows that to have an undistorted model, in the general case, Poisson’s ratio must be the same for the model and the “Prototype structure”, (Blazynski, 1983).

RESULT & ANALYSIS

Numerous tensile tests have been carried out made with plasticine. The plasticine paste was chosen a as commercial paste that has a limited ductility and tends to develop localised deformation. In the first part of the tensile test soft solids usually deform elastically. That is, if the load on the specimen is released, the specimen will return to its original length. In general, soft solids show a linear relationship between stress and strain in the elastic region of the

stress-strain diagram, which is described by Hooke’s Law,

  



= E (strain) or E = (units of Pa) (stress)

, where E is the modulus of elasticity, or Young’s modulus. In this test, an elongated specimen may be stretched and the load will be measured as a function of strain and strain rate.

The fundamental measures of the material properties are determined from a tensile test. The axial deformations resulting from an axial force on a long slender rod are frequently quoted using the engineering stress, , and engineering strain . The engineering stress and true stress are defined using the undeformed and instantaneous areas A0 and A respectively, as

       0 A P E 

, A0

P





where; P is the instantaneous load; A is the instantaneous cross-sectional area and A0 is the original cross-sectional area. The engineering strain can be represented as:

0 0 0 1 L d L L L E    

; where L1 is the instantaneous length, L0 is the original length and d is the

extension. Similarly the true strain can be represented as:

                0 0 0 0 1 1 ln ln ln = L d L d L L L 

where; L0 is the original length of the specimen and L is the instantaneous height. The true axial

strain rate is; L d

V L V          0 1 .



, where; Vch is the cross head velocity. The uniaxial stress,

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proportional to the strains. Whilst materials are elastic, the stress is proportional to the strain, according to the Hooke’s law. Within the elastic limits of materials, i.e. within the limits in which Hooke’s law applies, this also implies that the load is proportional to the

deformation:

C d A PL L

d A

P strain

stress

E      

0 0

0 0  

; These calculations provides evidence that, prior to the yield, the material response is elastic rather than viscoelastic. The amount of plasticity that a material can exhibit is a significant feature when evaluating its suitability. However, for the paste deformation processes, the more plastic a material is, the more it can be deformed without fracture. This ability of a material to change shape without fracture is known as the ductility.

Load vs. displacement. Stress vs. apparent strain. Stress vs. engineering strain.

Figure [2]: Showing the curves obtained by using EXCEL software with the given formulations.

The primary data, obtained from a tensile extension test, are those of the load and the corresponding displacement. For a particular geometry (thickness, breadth and length of the specimen), the extensive load is recorded as a function of the length extension. Typical examples of load vs displacement are shown in Figure [2], where the total load (N) is plotted against the displacement. The same data are shown on stress strain as shown in Figure [2] at various velocities, (Strain rates).

FINITE ELEMENT ANALYSIS (FEA)

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of finite size in the model. The term “finite element method”, was first introduced in solid mechanics applications, both used matrix displacement methods to solve plane stress problems with triangular and rectangular elements. Structural mechanics, continuum mechanics, flow and deformation are the main areas of application of finite element methods. Equilibrium problemsoften occur when the system does not vary with time of tensile test is represented in Figures [3 & 4], (Crisfield, 1986).

Figure [3]:- Representation Tensile specimen initially and final deformation.

To overcome the problem of discontinuities, (Zienkiewicz’s, 1994) pioneering work of adaptive mesh and mesh refinement led to the concept of ‘smart’ or ‘autonomous’ algorithms in computational mechanics. Zienkiewicz’s approach was to minimise the level of complexity in software development. To achieve this it is important to use a flexible data structure. This proves to be suitable for integrating structured & unstructured meshes for implementation of mesh adaptivity.

Figure [4]:- LUSASTM, (1999), Finite Element Analysis, Ltd., Kingston upon Thames, UK.

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the time dependence. However, the use of a powerful computer is essential to the success of finite element analysis.

Figure [5] :- The longitudinal strain distribution at specified time intervals, ELFEN, (1999).

Measurements of the distance that the deforming section of the specimen elongates, together with time records, can be used to determine the velocity of neck propagation in the specimen. The basic concepts and theory of the finite element method are explained and its ability to model various forming processes is discussed and reviewed. A brief introduction is given to the commercial finite element packages used in this study (ABAQUS, USA; ELFEN, Rockfield Software Limited, UK; LUSAS, FEA Limited, U.K.) to describe the tensile testing of soft solids w. r. t. pastes materials. Importantly, the validation of flow visualisation and FE methods are represented in Figures [5 & 6].

Figure [6]:- Lateral strain distribution at specified time intervals, Finite Element code ABAQUSTM (1995).

CONCLUSIONS

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approach has been successfully used to simulate the response of a soft-solids specimen when subject to a tensile load and later relaxation under constant displacement. Finally it has been shown that the FE analysis predicts the response for elastic-viscoplastic materials in simple deformation experiments. Commercially available finite element packages usually have a number of different elements available in the element library. For example, ABAQUS (1995)has nearly 400 different element variations, LUSAS (1999) has nearly 100 different element variations, and ELFEN (1999) has nearly 300 different element variations. The general formulation is based upon the assumption that linear elastic deformation occurs prior to yield and yield surface is strain rate hardening as defined by an associated viscoplastic flow rule, w. r. t. temporary (elastic) and permanent (plastic) deformation.

REFERENCES

1. “ABAQUS Theory Manual”, (1995), (Habbitt, Karlsson, and Sorensen, Inc., Providence, RI, USA, 383.

2. Blazynski, T.Z., (1983), “Applied Elasto-Plasticity of Solids”, Macmillan, London.

3. Crisfield, M.A., (1986), “Finite Elements and Solution Procedures for Structural Analysis”, Vol.1; Linear Analysis, Pineridge Press, Swansea.

4. ELFEN, (1999), Theory and Examples Manuals”, Rockfield Software Ltd., Innovation Centre, University of Wales, Swansea.

5. Hertzberg, R.W., (1996), “Deformation and Fracture Mechanics of Engineering Materials”, IIIrd. Edition, John Wiley & Sons, Inc., New-York.

6. LUSAS, (1999), “Theory and Example Manuals”, Finite Element Analysis Limited, Kingston-upon-Thames, Surrey.

7. Kalpakjian, S., (1984), “Manufacturing Processes for Engineering Materials”, Addison-Wesley Publishing Company, Inc., Reading, MA, USA, p. 386-652.

8. Kothari, D. C., (1999), “Measurement of RHEOLOGY of Pastes”, PhD Thesis, Imperial College of Engineering, Technology & Medicine, University of LONDON.