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Article
Publication date: 11 January 2021

Victor Rizov

This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic…

Abstract

Purpose

This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time.

Design/methodology/approach

Time-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results.

Findings

The variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived.

Originality/value

The time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

Details

World Journal of Engineering, vol. 18 no. 3
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 22 July 2022

Shafahat Ali, Said Abdallah, Deepak H. Devjani, Joel S. John, Wael A. Samad and Salman Pervaiz

This paper aims to investigate the effects of build parameters and strain rate on the mechanical properties of three-dimensional (3D) printed polylactic acid (PLA) by…

Abstract

Purpose

This paper aims to investigate the effects of build parameters and strain rate on the mechanical properties of three-dimensional (3D) printed polylactic acid (PLA) by integrating digital image correlation and desirability function analysis. The build parameters included in this paper are the infill density, build orientation and layer height. These findings provide a framework for systematic mechanical characterization of 3D-printed PLA and potential ways of choosing process parameters to maximize performance for a given design.

Design/methodology/approach

The Taguchi method was used to shortlist a set of 18 different combinations of build parameters and testing conditions. Accordingly, 18 specimens were 3D printed using those combinations and put through a series of uniaxial tensions tests with digital image correlation. The mechanical properties deduced for all 18 tests were then used in a desirability function analysis where the mechanical properties were optimized to determine the ideal combination of build parameters and strain rate loading conditions.

Findings

By comparing the tensile mechanical experimental properties results between Taguchi's recommended parameters and the optimal parameter found from the response table of means, the composite desirability had increased by 2.08%. The tensile mechanical properties of the PLA specimens gradually decrease with an increase in the layer height, while they increase with increasing the infill densities. On the other hand, the mechanical properties have been affected by the build orientation and the strain rate in similar increasing/decreasing trends. Additionally, the obtained optimized results suggest that changing the infill density has a notable impact on the overall result, with a contribution of 48.61%. DIC patterns on the upright samples revealed bimodal strain patterns rendering them more susceptible to failures because of printing imperfections.

Originality/value

These findings provide a framework for systematic mechanical characterization of 3D-printed PLA and potential ways of choosing process parameters to maximize performance for a given design.

Details

Rapid Prototyping Journal, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1355-2546

Keywords

Article
Publication date: 29 June 2022

Fan Lin, Jianshe Peng, Shifeng Xue and Jie Yang

In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear…

Abstract

Purpose

In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.

Design/methodology/approach

In this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.

Findings

The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.

Originality/value

The study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

Details

Multidiscipline Modeling in Materials and Structures, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 21 July 2022

Yajun Dai, Chang Liu, Min Zhan, Xiangyu Wang, Chao He and Qingyuan Wang

The investigations provide a basis for the optimization of the alloy 6061-T6 friction stir welding (FSW) process to improve the mechanical properties of welded joints.

17

Abstract

Purpose

The investigations provide a basis for the optimization of the alloy 6061-T6 friction stir welding (FSW) process to improve the mechanical properties of welded joints.

Design/methodology/approach

The local deformation of the FSW joint in tension and fatigue test were experimentally investigated by digital image correlation (DIC) technique.

Findings

The local stress-strain behaviors of the sub-regions show that the plastic strain always concentrated at the heat affected zone (HAZ) on the advancing side both in tension and high cycle fatigue and eventually leads to the final fracture. The evolution of the plastic strain at very low stress is extremely slow and accounts for most of the total fatigue life. However, the local deformation exhibits a sudden increase just before the fatigue failure.

Originality/value

Based on the experimental data, the result indicates that the HAZ is the weakest zone across the weld and the strain localization in high cycle fatigue is very harmful and unpredictable for the FSW joints.

Details

International Journal of Structural Integrity, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 1 April 1993

Y. TSUI and Y.M. CHENG

Large strain model can be formulated in terms of the Lagrangian or the Eulerian frame. In this paper, the Eulerian type large strain models are studied. Numerical examples…

Abstract

Large strain model can be formulated in terms of the Lagrangian or the Eulerian frame. In this paper, the Eulerian type large strain models are studied. Numerical examples on the Lagrangian and Eulerian types large strain models are investigated and compared. It is found that the differences in the choice of large strain model under large strain and rotation problems are noticeable but not significant if small load step is used for analysis. Furthermore, we have also found that unsymmetrical formulation instead of symmetrical formulation should be adopted for Eulerian type large strain models.

Details

Engineering Computations, vol. 10 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 January 2006

H. Rhee and K.N. Subramanian

To understand the roles of service‐related parameters, such as imposed cyclic strain amplitude and cyclic strain rate, on the stress relaxation behaviour of eutectic Sn‐Ag…

1005

Abstract

Purpose

To understand the roles of service‐related parameters, such as imposed cyclic strain amplitude and cyclic strain rate, on the stress relaxation behaviour of eutectic Sn‐Ag solder joints.

Design/methodology/approach

Cyclic shear straining with associated stress relaxation at the shear strain extremes imposed was carried out on pre‐strained eutectic Sn‐Ag solder joints with various cyclic shear straining conditions. Results from such experiments were compared with previously reported findings from monotonic shear straining and stress relaxation tests.

Findings

At higher testing temperatures with a larger cyclic strain amplitude, stress states realized at the subsequent cycle are comparable with, or even gradually increase on, those experienced at the previous cycle, especially after few cycles. The maximum shear stress obtained at each cycle and residual stress during stress relaxation are strongly affected by cyclic strain rate. Stress relaxation during subsequent cycles of straining was found to be strongly dependent on the test temperature, and the imposed cyclic strain amplitude and cyclic strain rate.

Originality/value

In this paper, the experiments were carried out on eutectic Sn‐Ag solder joints with about a 100 μm joint thickness, which are, therefore, representative of those used in microelectronics. Also, there is no systematic study reporting the effects of cyclic straining conditions on the stress relaxation behaviour of eutectic Sn‐Ag solder for this joint configuration in the published literature.

Details

Soldering & Surface Mount Technology, vol. 18 no. 1
Type: Research Article
ISSN: 0954-0911

Keywords

Article
Publication date: 1 December 2002

Yulan Zheng, John Atkinson and Russ Sion

This paper presents results of work aimed at characterising the zero offset stability in novel thick film strain gauges. The devices studied are z‐axis (k33) load sensors…

Abstract

This paper presents results of work aimed at characterising the zero offset stability in novel thick film strain gauges. The devices studied are z‐axis (k33) load sensors fabricated on insulated stainless steel substrates and include examples of novel commercially developed force sensors. Devices loaded with compressive strains using a purpose designed test jig were found to exhibit a significant zero offset shift, which is negative up to a certain level (typically 1,000 micro strains) and then increasingly positive when strained beyond this point. Repeated cycles of loading then produced a certain level of stability until the previous maximum value of applied strain was exceeded. Temperature coefficient of resistance (TCR) measurements showed the devices to exhibit characteristics that depend significantly on the device geometry. The TCR was found to increase positively with increasing device thickness and surface area. The effect of overglazing the devices was found to decrease the TCR.

Details

Microelectronics International, vol. 19 no. 3
Type: Research Article
ISSN: 1356-5362

Keywords

Article
Publication date: 23 January 2009

Yan Yu and Jinping Ou

The purpose of this paper is to describe a wireless strain sensor system which will allow easier collection of accurate strain signals in civil engineering structures. The…

Abstract

Purpose

The purpose of this paper is to describe a wireless strain sensor system which will allow easier collection of accurate strain signals in civil engineering structures. The sensor system is developed by integrating with resistance strain gauge, and the data fusion method is proposed based on batch estimation theory.

Design/methodology/approach

The principle of resistance strain gauge is discussed and the project of wireless acquisition system of strain signal is given. Wireless strain sensor is integrated with modularization method. Based on batch estimation theory, the data fusion method of strain signal is described. The experiment of wireless strain sensor system is finished on a typical concrete beam structure, the measure data processed by using the data fusion method and the arithmetic average value method is compared and analyzed.

Findings

The research result shows that the wireless strain sensor can be installed easily and thus is applied compatibly to local monitoring in civil engineering. The strain signal processed by the data fusion method is more accurate than the one processed by the arithmetic average value method, and thus the proposed data fusion method is fit for processing such slowly‐changing signals as strain.

Originality/value

In this paper, the innovation is shown from two views: one is applying wireless technique to collect strain signals; another is that data fusion with wide application can make measurements more precise and reliable by eliminating uncertain value than using the arithmetic average value method. In general, the developed wireless sensor system and the proposed data fusion method are fit for local monitoring.

Details

Sensor Review, vol. 29 no. 1
Type: Research Article
ISSN: 0260-2288

Keywords

Article
Publication date: 1 March 1985

Balkrishna S. Annigeri, Brice N. Cassenti and Anthony J. Dennis

The kinematics of small and large deformations (displacements, rotations and strains) is described by use of the engineering strain, the logarithmic strain, the Seth‐Hill…

Abstract

The kinematics of small and large deformations (displacements, rotations and strains) is described by use of the engineering strain, the logarithmic strain, the Seth‐Hill class of strains and the rate‐type strains derived using the Lagrangian and the ‘Relative’ descriptions. The displacement gradient is computed for two and three dimensions and the error associated with use of the small rotation approximation is plotted. The components of the rotation tensor are derived for a four‐noded isoparametric quadrilateral finite element for determining the error due to small displacement and rotation approximations. Finally, the various strain measures are computed and plotted for representative problems.

Details

Engineering Computations, vol. 2 no. 3
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 March 2007

K. Kadirgama, K.A. Abou‐El‐Hossein, B. Mohammad and H. Habeeb

The Finite Element Method and Response Surface Method are used to find the effect of milling parameters (Cutting speed, Feedrate and Axial depth) on plastic strain when…

Abstract

The Finite Element Method and Response Surface Method are used to find the effect of milling parameters (Cutting speed, Feedrate and Axial depth) on plastic strain when milling Hastelloy C‐22HS. This simulation gain more understanding of the strain distribution in metal cutting. Response surface method (RSM) has been used to minimize the number of simulation. The contour plot from the RSM shows the relationship between variables (cutting speed, feedrate and axial depth) and response (plastic strain ‐ rate).The friction interaction along the tool‐chip interface is modeled with Coulomb friction law.

Details

Multidiscipline Modeling in Materials and Structures, vol. 3 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

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