On determination of material parameters from loading and unloading responses in nanoindentation with a single sharp indenter

2006 ◽  
Vol 21 (4) ◽  
pp. 995-1011 ◽  
Author(s):  
Lugen Wang ◽  
S.I. Rokhlin
Keyword(s):  
Finite Element ◽  
Strain Hardening ◽  
Yield Stress ◽  
Finite Element Simulations ◽  
Strain Hardening Exponent ◽  
Scaling Functions ◽  
Stress And Strain ◽  
Wide Range ◽  
Loading And Unloading

This paper quantitatively describes the loading-unloading response in nanoindentation with sharp indenters using scaling analyses and finite element simulations. Explicit forward and inverse scaling functions for an indentation unloading have been obtained and related to those functions for the loading response [L. Wang et al., J. Material Res.20(4), 987–1001 (2005)]. The scaling functions have been obtained by fitting the large deformation finite element simulations and are valid from the elastic to the full plastic indentation regimes. Using the explicit forward functions for loading and unloading, full indentation responses for a wide range of materials can be obtained without use of finite element calculations. The corresponding inverse scaling functions allow one to obtain material properties from the indentation measurements. The relation between the work of indentation and the ratio between hardness and modulus has also been studied. Using these scaling functions, the issue of nonuniqueness of the determination of material modulus, yield stress, and strain-hardening exponent from nanoindentation measurements with a single sharp indenter has been further investigated. It is shown that a limited material parameter range in the elastoplastic regime can be defined where the material modulus, yield stress, and strain-hardening exponent may be determined from only one full indentation response. The error of such property determination from scattering in experimental measurements is determined.

Inverse scaling functions in nanoindentation with sharp indenters: Determination of material properties

2005 ◽  
Vol 20 (4) ◽  
pp. 987-1001 ◽  
Author(s):  
Lugen Wang ◽  
M. Ganor ◽  
S.I. Rokhlin
Keyword(s):  
Finite Element ◽  
Strain Hardening ◽  
Yield Stress ◽  
Material Properties ◽  
Contact Stiffness ◽  
Experimental Parameter ◽  
Inversion Method ◽  
Strain Hardening Exponent ◽  
Scaling Functions ◽  
Scaling Analysis

This paper, based on extensive finite element simulations and scaling analysis, presents scaling functions for the inverse problem in nanoindentation with sharp indenters to determine material properties from nanoindentation response. All the inverse scaling functions were directly compared with results calculated using the large deformation finite element method and are valid from the elastic to the full plastic regimes. To relate the material properties to measurable indentation parameters a new nondimensional experimental parameter Λ=P/(DS) was introduced, where P is load, D is indentation depth, and S is contact stiffness. This parameter is monotonically related to the ratio of yield stress to modulus. The modulus, hardness and yield stress are presented as explicit functions of Λ and the strain hardening exponent. The error in the inverse modulus, hardness, and yield stress due to uncertainty of the strain hardening exponent was studied and is compared with that of the traditional Oliver–Pharr method. The method of determining the strain hardening exponent from measurement with an additional indenter with a different cone apex angle is described. For this, a scaling function with the strain hardening exponent as the only unknown was obtained. In this way, the modulus, hardness, yield stress and strain hardening exponent may be determined. Experimental results show the inversion method permits the modulus and hardness to be accurately determined irrespective of the effects of pileup or sink-in.

Determination of Stress-Strain Constitutive Relation of Echelle Grating Al Film by Nanoindentation Test and Simulation

2012 ◽  
Vol 625 ◽  
pp. 312-317 ◽  
Author(s):  
Guang Feng Shi ◽  
Guo Quan Shi ◽  
Lin Sen Song ◽  
Zhi Wei Xu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Strain Hardening ◽  
Yield Stress ◽  
Strain Hardening Exponent ◽  
Stress And Strain ◽  
Stress Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Echelle Grating

For the research on elastic-plastic deformation characteristics of the echelle grating in the mechanical ruling depth range, a series of nanoindentation tests are completed about the deposited Al film of available echelle grating with a Berkovich indenter on a CSM nanoindentation instrument. Then a finite element analysis of the nanoindentation process is studied with an orthogonal experiment method for a series of given parameters containing the yield stress and strain-hardening exponent. The optimum combinations of yield stress and strain-hardening exponent are 200MPa and 0.1, which are got by the objective of the least absolute value of maximum loads deviation between the indentation test and the finite element analysis. Finally the elastic-plastic stress-strain curve of power function of the Al film is represented with the difference analysis from the orthogonal simulations.

Effect of Modulations on Yield Stress and Strain Hardening Exponent of Solution Treated Cu-Ti Alloys

1998 ◽  
Vol 38 (9) ◽  
pp. 1469-1474 ◽  
Author(s):  
S. Nagarjuna ◽  
M. Srinivas ◽  
K. Balasubramanian ◽  
D.S. Sarma
Keyword(s):  
Strain Hardening ◽  
Yield Stress ◽  
Strain Hardening Exponent ◽  
Stress And Strain ◽  
Ti Alloys ◽  
Solution Treated

scholarly journals Relationship Between Rockwell C Hardness and Inelastic Material Constants

2002 ◽  
Vol 124 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Akihiko Hirano ◽  
Masao Sakane ◽  
Naomi Hamada
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Strain Hardening ◽  
Yield Stress ◽  
Plastic Material ◽  
Stress And Strain ◽  
Material Constants ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Hardening Coefficient

This paper describes the relationship between Rockwell C hardness and elastic-plastic material constants by using finite element analyses. Finite element Rockwell C hardness analyses were carried out to study the effects of friction coefficient and elastic-plastic material constants on the hardness. The friction coefficient and Young’s modulus had no influence on the hardness but the inelastic materials constants, yield stress, and strain hardening coefficient and exponent, had a significant influence on the hardness. A new equation for predicting the hardness was proposed as a function of yield stress and strain hardening coefficient and exponent. The equation evaluated the hardness within a ±5% difference for all the finite element and experimental results. The critical thickness of specimen and critical distance from specimen edge in the hardness testing was also discussed in connection with JIS and ISO standards.

Study of plastically deformed region underneath the ball in indentation tests and evaluation of mechanical properties of materials through finite element simulation and a hybrid algorithm

2020 ◽  
pp. 095440622093294
Author(s):  
Mahendra K Samal ◽  
A Syed ◽  
RN Khatri ◽  
J Chattopadhyay
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Plastic Strain ◽  
Strain Hardening ◽  
Yield Stress ◽  
Hybrid Algorithm ◽  
Equivalent Plastic Strain ◽  
Stress And Strain ◽  
Ball Indentation ◽  
Indentation Tests

Ball indentation technique has been studied extensively in literature and it has been widely applied to determine mechanical properties of different materials because of simplicity and minimal requirement of material for the tests. Originally, the material deformation was represented in terms of a representative strain, which is a non-dimensional form of indentation diameter and a representative stress, which again is the instantaneous mean pressure multiplied by some empirical factors. It is known that the state of deformation as well as stress beneath the ball is multiaxial in nature in a ball indentation test. In this work, a new hybrid algorithm for estimation of equivalent stress and equivalent plastic strain during the process of indentation in the most stressed location beneath the ball has been developed. The algorithms uses experimental load–indentation data as well as the multiaxial stress and strain parameters obtained from 2D axisymmetric elastic-plastic finite element simulations. The stress and strain multiaxial parameters are functions of applied load, material yield stress and strain hardening exponents. The algorithm is iterative in nature and uses suitable initial guess values for material yield stress and strain hardening exponents and it converges very quickly. This method can be applied to determine the material stress–strain curve for a wide range of equivalent plastic strain, yield stress as well as plastic strain hardening exponent of the engineering materials. The data points of load vs. indentation depth as obtained directly from the ball indentation tests can be used in the new algorithm without the need for conducting unloading during the test. To illustrate the new scheme, two case studies have been presented where the results from the proposed new method have been compared with those of the existing method in literature and tensile test data to check the accuracy.

Anomaly of the Work Hardening of Zn-Cu Single Crystals Oriented for Slip in Secondary Systems

2011 ◽  
Vol 56 (4) ◽  
pp. 1021-1027
Author(s):  
K. Pieła
Keyword(s):  
Strain Hardening ◽  
Single Crystals ◽  
Yield Stress ◽  
Work Hardening ◽  
Temperature Anomaly ◽  
Strain Hardening Exponent ◽  
Plastic Behavior ◽  
Thermal Dependence ◽  
Copper Addition ◽  
Secondary Systems

Anomaly of the Work Hardening of Zn-Cu Single Crystals Oriented for Slip in Secondary SystemsThe copper alloyed (up to 1.5%) zinc single crystals oriented for slip in non-basal systems (orientation close to < 1120 >) were subjected to compression test within a range of temperatures of 77-293K. It has been stated, that Zn-Cu crystals exhibit characteristic anomalies of the thermal dependence of yield stress and of the strain hardening exponent. Both of them are related to the change in type and sequence of active non-basal slip systems: pyramidal of the 1storder {1011} < 1123 > (Py-1) and pyramidal of the 2ndorder {1122} < 1123 > (Py-2). The temperature anomaly of the yield stress results from the change of the slip from Py-2 systems to simultaneous slip in the Py-2 and Py-1 (Py-2 + Py-1) systems, occurring in the preyielding stage. On the other hand, sequential activation of pyramidal systems taking place in advanced plastic stage (i.e. the first Py-2 and next Py-2 + Py-1 systems) is responsible for temperature anomaly of strain hardening exponent. Increase in copper addition favors the activity of Py-2 systems at the expense of Py-1 slip, what leads to a drastic differences in plastic behavior of zinc single crystals.

A Compliant Transmission Mechanism With Intermittent Contacts for Cycle-Doubling

2006 ◽  
Vol 129 (1) ◽  
pp. 114-121 ◽  
Author(s):  
Nilesh D. Mankame ◽  
G. K. Ananthasuresh
Keyword(s):  
Finite Element ◽  
Conceptual Design ◽  
Finite Element Simulations ◽  
Nonlinear Finite Element ◽  
Transmission Mechanism ◽  
Input Frequency ◽  
Length Scales ◽  
Wide Range ◽  
Macro Scale ◽  
Functional Prototype

A novel compliant transmission mechanism that doubles the frequency of a cyclic input is presented in this paper. The compliant cycle-doubler is a contact-aided compliant mechanism that uses intermittent contact between itself and a rigid surface. The conceptual design for the cycle-doubler was obtained using topology optimization in our earlier work. In this paper, a detailed design procedure is presented for developing the topology solution into a functional prototype. The conceptual design obtained from the topology solution did not account for the effects of large displacements, friction, and manufacturing-induced features such as fillet radii. Detailed nonlinear finite element analyses and experimental results from quasi-static tests on a macro-scale prototype are used in this paper to understand the influence of the above factors and to guide the design of the functional prototype. Although the conceptual design is based on the assumption of quasi-static operation, the modified design is shown to work well in a dynamic setting for low operating frequencies via finite element simulations. The cycle-doubler design is a monolithic elastic body that can be manufactured from a variety of materials and over a range of length scales. This makes the design scalable and thus adaptable to a wide range of operating frequencies. Explicit dynamic nonlinear finite element simulations are used to verify the functionality of the design at two different length scales: macro (device footprint of a square of 170mm side) at an input frequency of 7.8Hz; and meso (device footprint of a square of 3.78mm side) at an input frequency of 1kHz.

scholarly journals Large elastic deformations of isotropic materials. I. Fundamental concepts

1948 ◽  
Vol 240 (822) ◽  
pp. 459-490 ◽  
Keyword(s):  
The Body ◽  
Elastic Behaviour ◽  
Stress And Strain ◽  
Elastic Deformations ◽  
Hooke’S Law ◽  
Widespread Agreement ◽  
Wide Range ◽  
Hooke's Law ◽  
High Degree

The mathematical theory of small elastic deformations has been developed to a high degree of sophistication on certain fundamental assumptions regarding the stress-strain relationships which are obeyed by the materials considered. The relationships taken are, in effect, a generalization of Hooke’s law— ut tensio, sic vis . The justification for these assumptions lies in the widespread agreement of experiment with the predictions of the theory and in the interpretation of the elastic behaviour of the materials in terms of their known structure. The same factors have contributed to our appreciation of the limitations of these assumptions. The principal problems, which the theory seeks to solve, are the determination of the deformation which a body undergoes and the distribution of stresses in it, when certain forces are applied to it, and when certain points of the body are subjected to specified displacements. These problems are always dealt with on the assumption that the generalization of Hooke’s law is obeyed by the material of the body and that the deformation is small, i.e. the change of length, in any linear element in the material, is small compared with the length of the element in the undeformed state. Apart from the fact that the generalization of Hooke’s law is obeyed accurately by a very wide range of materials, under a considerable variety of stress and strain conditions, it has the further advantage that it leads to a mathematically tractable theory.

Effect of Steel Properties on Buckling Pressure of Corroded Pipelines

2017 ◽  
Vol 898 ◽  
pp. 741-748 ◽  
Author(s):  
Meng Li ◽  
Hong Zhang ◽  
Meng Ying Xia ◽  
Kai Wu ◽  
Jing Tian Wu ◽  
...  
Keyword(s):  
Finite Element ◽  
Yield Strength ◽  
Strain Hardening ◽  
Corrosion Damage ◽  
Element Model ◽  
External Pressure ◽  
Strain Hardening Exponent ◽  
The Finite Element Method ◽  
Collapse Pressure ◽  
Steel Properties

Due to the harsh environment for submarine pipelines, corrosion damage of the pipeline steels is inevitable. After the corrosion damage, pipelines are prone to failure and may cause serious consequences. The analysis of the effects of different steel properties on the collapse pressure of pipelines with corrosion defects is of importance for the option of appropriate pipeline and avoiding accidents. Based on the finite element method, the finite element model of the pipeline with defects under external pressure was built. Firstly, the accuracy of the numerical model was validated by comparing with previous experimental results. The effects of yield strength and strain hardening exponent on collapse pressure of pipelines with different sizes of defect were discussed in detail. Results showed that the yield strength and strain hardening exponent have different influences on collapse pressure: the collapse pressure increases with the increasing yield strength, and the collapse pressure decreases with the increasing strain hardening exponent.

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