Nonlinear Stress–Strain Characterization of Cast Iron Used to Manufacture Pipes for Water Supply

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Balvant Rajani
Keyword(s):  
New York ◽  
Cast Iron ◽  
Water Supply ◽  
Mechanical Design ◽  
Constitutive Law ◽  
Uniaxial Tensile ◽  
Normal Strain ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Compressive Tests

The stress–strain response of cast iron under tension or compression is nonlinear. This paper examines how the hyperbolic constitutive law can be applied to characterize nonlinear stress–strain behavior of cast iron used in water supply networks. Procedures are described to obtain parameters of the hyperbolic constitutive law from either the response (data) obtained from simple uniaxial tensile and compressive tests or from bending tests. To demonstrate its applicability, this hyperbolic constitutive law is first applied to data obtained from uniaxial tensile and compressive tests conducted by Schlick and Moore (1936, “Strength and Elastic Properties of Cast Iron in Tension, Compression, Flexure, and Combined Tension and Flexure,” Bulletin 127, Iowa Engineering Experiment Station, Ames, IA). In addition, an approach to extract parameters for the hyperbolic constitutive law from bending (beam and pipe rings) tests is proposed and subsequently applied to tests conducted by Talbot (1908, “Tests of Cast-Iron and Reinforced Concrete Culvert Pipe,” Bulletin No. 22, University of Illinois, Urbana, IL). This latter approach is attractive for practical purposes because the test set up is simple and the test coupons are very easy to prepare. The hyperbolic constitutive law in conjunction with maximum normal strain theory as proposed by St. Venant (Collins, J. A., 1993, Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, John Wiley, New York, NY) was also used to predict failure loads.

Studies on the Stress-Strain Relationship Bovine Cortical Bone Based on Ramberg–Osgood Equation

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
N. K. Sharma ◽  
M. D. Sarker ◽  
Saman Naghieh ◽  
Daniel X. B. Chen
Keyword(s):  
Cortical Bone ◽  
Linear Regression Analysis ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Loading Conditions ◽  
Stress Strain ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Strain Relationship ◽  
Relationship Of

Bone is a complex material that exhibits an amount of plasticity before bone fracture takes place, where the nonlinear relationship between stress and strain is of importance to understand the mechanism behind the fracture. This brief presents our study on the examination of the stress–strain relationship of bovine femoral cortical bone and the relationship representation by employing the Ramberg–Osgood (R–O) equation. Samples were taken and prepared from different locations (upper, middle, and lower) of bone diaphysis and were then subjected to the uniaxial tensile tests under longitudinal and transverse loading conditions, respectively. The stress–strain curves obtained from tests were analyzed via linear regression analysis based on the R–O equation. Our results illustrated that the R–O equation is appropriate to describe the nonlinear stress–strain behavior of cortical bone, while the values of equation parameters vary with the sample locations (upper, middle, and lower) and loading conditions (longitudinal and transverse).

The Role of Flow-Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage

2001 ◽  
Vol 123 (5) ◽  
pp. 410-417 ◽  
Author(s):  
Chun-Yuh Huang ◽  
Van C. Mow ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Viscoelastic Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Molecular Organization ◽  
Solid Matrix ◽  
Uniaxial Tensile ◽  
Elastic Model ◽  
Compressive Properties ◽  
Stress Strain

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension–compression stress–strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102, pp. 73–84] to incorporate tension–compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122, pp. 576–586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37, pp. 1–38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123–130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension–compression nonlinearity.

Measurement of the Constitutive Behavior of Underfill Encapsulants

2003 ◽  
Author(s):  
M. Saiful Islam ◽  
Jeffrey C. Suhling ◽  
Pradeep Lall
Keyword(s):  
Flip Chip ◽  
Mechanical Response ◽  
Capillary Flow ◽  
Mechanical Test ◽  
Testing Machine ◽  
Production Equipment ◽  
Uniaxial Tensile ◽  
Stress Strain ◽  
Strain Behavior ◽  
Nonlinear Stress

Reliable, consistent, and comprehensive material property data are needed for microelectronic encapsulants for the purpose of mechanical design, reliability assessment, and process optimization of electronic packages. In our research efforts, the mechanical responses of several different capillary flow snap cure underfill encapsulants are being characterized. A microscale tension-torsion testing machine has been used to evaluate the uniaxial tensile stress-strain behavior of underfill materials as a function of temperature, strain rate, specimen dimensions, humidity, thermal cycling exposure, etc. A critical step to achieving accurate experimental results has been the development of a sample preparation procedure that produces mechanical test specimens that reflect the properties of true underfill encapsulant layers. In the developed method, 75–125 μm (3–5 mil) thick underfill uniaxial tension specimens are dispensed and cured using production equipment and the same processing conditions as those used with actual flip chip assemblies. Although several underfills have been examined, this work features results for the mechanical response of a single typical capillary flow snap cure underfill. A three parameter hyperbolic tangent empirical model has been shown to provide accurate fits to the observed underfill nonlinear stress-strain behavior over a range of temperatures and strain rates. In addition, typical creep data are presented.

Material properties for fracture mechanics based strength assessment of cast iron water mains

2021 ◽  
Vol 48 (1) ◽  
pp. 62-74
Author(s):  
Suborno Debnath ◽  
Ismail M. Ali ◽  
Ashutosh Sutra Dhar ◽  
Premkumar Thodi
Keyword(s):  
Cast Iron ◽  
Fracture Mechanics ◽  
Distribution Systems ◽  
Water Distribution ◽  
Structural Integrity ◽  
Uniaxial Tensile ◽  
Stress Strain ◽  
Strength Assessment ◽  
Integrity Assessment ◽  
Water Mains

Municipal water distribution systems in Canada and other countries include a large number of cast iron pipes that were installed almost 50 years ago. For structural integrity assessment of these pipes, the fracture mechanics approach is found to be more effective than the conventional continuum mechanics-based approach. This paper presents the mechanical properties for fracture mechanics-based strength assessment of water mains determined through testing of cast iron pipes exhumed from two cities in Canada. Microstructure analysis is conducted to understand the materials’ inherent properties. Uniaxial tensile tests are conducted to determine the stress–strain relations. The influence of the rate of loading on stress–strain behaviour and loading-unloading responses are investigated. A simplified single-edge notch beam test is used to obtain the fracture toughness. Probabilistic distributions of the parameters are provided to account for the uncertainty and variabilities observed in the test results.

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