Prediction of Creep Behavior from Stress Relaxation Data for Nonlinearly Viscoelastic Materials

1978 ◽  
Vol 51 (1) ◽  
pp. 117-125 ◽  
Author(s):  
L. M. Wu ◽  
E. A. Meinecke ◽  
B. C. Tsai
Keyword(s):  
Stress Relaxation ◽  
Creep Behavior ◽  
Strain Curve ◽  
Relaxation Modulus ◽  
Polymeric Materials ◽  
Viscoelastic Materials ◽  
Relaxation Data ◽  
Stress Strain ◽  
Straight Line ◽  
Simple Fashion

Abstract The stress relaxation behavior of many polymeric materials can be expressed in a very simple fashion, because the logarithm of nominal stress fi(t) (based upon the undeformed cross-sectional area of the sample) plotted against the logarithm of time, t, is a straight line. Furthermore, these lines are often parallel, and with linearly viscoelastic materials, one obtains a straight line for the stress-relaxation modulus E(t)=fi(t)/εi, independent of the strain level. Thus, the linear stress-relaxation modulus can be expressed as: Ei(t)=Ei0·t−m, with Ei0 the modulus at t=1 s and m the slope of the straight line in the double logarithmic plot. Most polymers are, of course, nonlinearly viscoelastic (except for infinitesimal deformations); that is, the stress-relaxation modulus is a function of both time and strain. These time and strain effects can be factored out, if the log fi(t) versus log t curves are parallel: Ei(t,εi)=Ei0·t−mϕ(ε), where ϕ(ε), the strain function, is a measure of the nonlinearity of the viscoelastic response. It has been shown elsewhere that Ei0/ϕ(ε) is approximately identical to the modulus observed in the stress-strain measurement. With many polymers, creep experiments also yield approximately straight lines of slope n, when the logarithm of strain εi(t) is plotted against the logarithm of time. With nonlinearly viscoelastic materials, one generally does not obtain a set of parallel lines, when the stress fi, is changed. Therefore, it is not possible to separate the influence of time and stress on the creep compliance Di(t)=εi(t)/fi, as was the case for stress relaxation. It has been shown previously that the creep behavior can be predicted from stress-relaxation data with the help of the convolution integral. The numerical method involved is very laborious, however. It has been shown that the rate of creep may be predicted from the slope of stress-relaxation curves and the shape of the stress-strain curve. The purpose of this paper is to present a method by which the creep behavior of nonlinearly viscoelastic materials can be predicted in a simple fashion from stress-relaxation data. The theoretical predictions have been tested with the stress-relaxation and creep data of a block copolymer.

scholarly journals Mechanical Properties and Microstructural Collagen Alignment of the Ulnar Collateral Ligament During Dynamic Loading

2018 ◽  
Vol 47 (1) ◽  
pp. 151-157 ◽  
Author(s):  
Matthew V. Smith ◽  
Ryan M. Castile ◽  
Robert H. Brophy ◽  
Ashvin Dewan ◽  
David Bernholt ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Real Time ◽  
Strain Curve ◽  
Ulnar Collateral Ligament ◽  
Collagen Fibers ◽  
Stress Strain Curve ◽  
Collateral Ligament ◽  
Stress Strain ◽  
Collagen Organization ◽  
Collagen Alignment

Background: The ulnar collateral ligament (UCL) microstructural organization and collagen fiber realignment in response to load are unknown. Purpose/Hypothesis: The purpose was to describe the real-time microstructural collagen changes in the anterior bundle (AB) and posterior bundle (PB) of the UCL with tensile load. It was hypothesized that the UCL AB is stronger and stiffer with more highly aligned collagen during loading when compared with the UCL PB. Study Design: Descriptive laboratory study. Methods: The AB and PB from 34 fresh cadaveric specimens were longitudinally sectioned to allow uniform light passage for quantitative polarized light imaging. Specimens were secured to a tensile test machine and underwent cyclic preconditioning, a ramp-and-hold stress-relaxation test, and a quasi-static ramp to failure. A division-of-focal-plane polarization camera captured real-time pixelwise microstructural data of each sample during stress-relaxation and at the zero, transition, and linear points of the stress-strain curve. The SD of the angle of polarization determined the deviation of the average direction of collagen fibers in the tissue, while the average degree of linear polarization evaluated the strength of collagen alignment in those directions. Since the data were nonnormally distributed, the median ± interquartile range are presented. Results: The AB has larger elastic moduli than the PB ( P < .0001) in the toe region (median, 2.73 MPa [interquartile range, 1.1-5.6 MPa] vs 0.65 MPa [0.44-1.5 MPa]) and the linear region (13.77 MPa [4.8-40.7 MPa] vs 1.96 MPa [0.58-9.3 MPa]). The AB demonstrated larger stress values, stronger collagen alignment, and more uniform collagen organization during stress-relaxation. PB collagen fibers were more disorganized than the AB during the zero ( P = .046), transitional ( P = .011), and linear ( P = .007) regions of the stress-strain curve. Both UCL bundles exhibited very small changes in collagen alignment (SD of the angle of polarization) with load. Conclusion: The AB of the UCL is stiffer and stronger, with more strongly aligned and more uniformly oriented collagen fibers, than the PB. The small changes in collagen alignment indicate that the UCL response to load is due more to its static collagen organization than to dynamic changes in collagen alignment. Clinical Relevance: The UCL collagen organization may explain its susceptibility to injury with repetitive valgus loads.

Real-time cutting simulation in virtual reality systems based on the measurement of porcine organs

SIMULATION ◽  
2017 ◽  
Vol 93 (12) ◽  
pp. 1073-1085 ◽  
Author(s):  
YiDong Bao ◽  
DongMei Wu
Keyword(s):  
Stress Relaxation ◽  
Soft Tissues ◽  
Organ Specificity ◽  
Relaxation Data ◽  
Stress Strain ◽  
Pig Liver ◽  
Cutting Simulation ◽  
Virtual Operation ◽  
Liver And Kidney ◽  
Cutting Model

A virtual soft tissues cutting model consistent with the organ specificity of real soft tissues was established in this paper, which was applied to the virtual operation training system. A measurement platform of soft tissue organ was designed and built, and the stress–strain and stress–relaxation data of pig liver and kidney were experimentally measured. Then, using the viscoelasticity mathematical formula, an improved virtual cutting model of the meshless classified balls-filling was constructed through VC++ and OpenGL. The cutting performance of the virtual soft tissues was further increased by leveraging the improved cutting classification algorithm. Finally, the extrusion and cutting simulation was enabled through the force feedback device, and the accuracy and effectiveness of this cutting model were validated by a comparative study of the virtual soft tissues cutting model and the stress–strain and stress–relaxation data of pig liver and kidney.

Thermal Expansion And Viscoelastic Properties Of A Semi-Rigid Polyimide

1991 ◽  
Vol 227 ◽  
Author(s):  
Thor L. Smith ◽  
Churl S. Kim
Keyword(s):  
Liquid Crystalline ◽  
Linear Expansion ◽  
Tensile Modulus ◽  
Strain Curve ◽  
Relaxation Modulus ◽  
Superposition Method ◽  
Thermal Coefficient ◽  
Fixed Rate ◽  
Stress Strain ◽  
Ultimate Elongation

ABSTRACTStudies were made of the physical properties of the commercially available polyimide Upilex-SGA, which is prepared from biphenyl dianhydride and p-phenylene diamine. Annealing the Upilex-SGA for 2 hr Linder N2 at 400°C gave a film that expanded continuously when heated at a fixed rate, in contrast to the as-received film. The linear expansion showed a change of slope at 84°C and also at 295°C, the later being Tg. The thermal coefficient of linear expansion at all temperatures was very small, even above 295°C it is 27.8 × 10−6. Its stress-strain curve did not exhibit a yield point, even though its ultimate elongation is ˜23%. Similar behavior is shown by the PMDA-ODA polyimide, except its ultimate elongation is ˜70%,. The unusual stress- strain curves exhibited by these polyimides is undoubtedly caused by their liquid-crystalline morphology. The stress-relaxation modulus was measured at 0.5% extension and 12 temperatures from 30 to 330°C. Derived isochrones showed that the 1-s tensile modulus at 20°C is 9.0 GPa, but at 330°C it is 2.0 GPa. Creep curves were also measured at a stress of 30 MPa and at 10 temperatures from 30 to 340° C. Master curves prepared from the relaxation and creep data are discussed briefly and evidence is given which, show that the superposition method is not truly valid for this polyimide, which actually is not surprising.

Indentation Creep and Relaxation Measurements of Polymers

2004 ◽  
Vol 841 ◽  
Author(s):  
Mark R. VanLandingham ◽  
Peter L. Drzal ◽  
Christopher C. White
Keyword(s):  
Stress Relaxation ◽  
Mechanical Response ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Polymeric Materials ◽  
Indentation Creep ◽  
Dimethyl Siloxane ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Creep And Stress Relaxation

ABSTRACTInstrumented indentation was used to characterize the mechanical response of polymeric materials. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for creep compliance and stress relaxation modulus for epoxy, poly(methyl methacrylate) (PMMA), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison to the indentation creep and stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than rheometry values. Additional study of the deformation remaining in epoxy after creep testing revealed that a large portion of the creep displacement measured was due to post-yield flow. Indentation creep measurements of the epoxy using a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the PDMS were mainly linear elastic, but the filled PDMS exhibited some time-dependence and nonlinearity in both rheometry and indentation measurements.

scholarly journals Torsional hysteresis of mild steel

1917 ◽  
Vol 93 (651) ◽  
pp. 313-332 ◽  
Keyword(s):  
Mild Steel ◽  
Yield Point ◽  
Elastic Limit ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Straight Line ◽  
Straight Portion ◽  
Strain Axis ◽  
Inferior Limit

The stress-strain curve from no load to fracture for mild steel as usually obtained consists of three parts: (1) A straight line, followed by a part deviating only slightly from this straight portion; (2) a sharp bend, followed by a part approximately parallel to the strain axis; and (3) a curved rising part, leading ultimately to the breaking point. It is generally assumed that Hooke’s Law holds throughout the part (1), and is immediately followed by the sharply defined bend which constitutes the yield point. For mild steel first stressed in tension and then in compression, or subjected to positive and then negative torsional stresses, the stress-strain curve within a considerable range of stress is also supposed to be a straight line. It is further well known that if mild steel is stressed in tension beyond the yield point the elastic limit is raised, but only at the expense of lowering it in compression; or, if it is twisted beyond the yield point in one direction, its elastic limit is raised for stresses in that direction, but lowered for those in the opposite direction. Attempts have been made to relate the range of stress through which the stress-strain curve is a straight line with that through which a material, such as mild steel, can be stressed an infinite number of times without fracture. This is expressed by the well known Bauschinger’s Law, which, as stated by Mr. Leonard Bairstow, is as follows:—“The superior limit of elasticity can be raised or lowered by cyclical variations of stress, and at the inferior limit of elasticity will be raised or lowered by a definite, but not necessarily the same, amount. The range of stress between the two elastic limits has therefore a value which depends only on the material and the stress at the inferior limit of elasticity. This elastic range of stress is the same in magnitude as the maximum range of stress, which can be repeatedly applied to a bar without causing fracture, no matter how great the number of repetitions.”

Improving elastic modulus measurements for rock based on geology

2000 ◽  
Vol 6 (4) ◽  
pp. 333-346 ◽  
Author(s):  
Paul M. Santi ◽  
Jason E. Holschen ◽  
Richard W. Stephenson
Keyword(s):  
Elastic Modulus ◽  
Strain Curve ◽  
Elastic Behavior ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Rock Types ◽  
Plastic Materials ◽  
Straight Line ◽  
Elastic Plastic Materials ◽  
Engineering Projects

Abstract Since many engineering projects in rock never mobilize strengths near the uniaxial compressive strength (UCS) of the rock, elastic modulus becomes a critical parameter to describe the rock's behavior under loading. There are a number of methods available for calculating the elastic modulus from laboratory test data, and each method gives a slightly different value. The objective of this study is to evaluate the most repeatable method for each of a number of rock types, and then to develop guidelines to aid the practitioner in selecting the best method as a function of rock behavior. UCS tests were performed on 78 samples of nine rock types, including two basalts, two granites, two limestones, a quartzite, a sandstone, and a gypsum. Elastic moduli were calculated using six different methods reported in the literature or modified for this study. The modified secant and modified secant-at-50-percent-strength moduli (modified by shifting the origin to best intercept the extension of the main straight-line portion of the stress-strain curve) were the most repeatable methods for rocks with elastic and plastic-elastic behavior. Elastic-plastic materials, which have a broad concave-downward stress-strain curve, are best evaluated using the tangent modulus on the upper of two distinct straight-line segments. For materials which show creep or extended plastic deformation with no sharp failure, the secant-at-50-percent-strength modulus and modified secant-at-50-percent-strength modulus are the most repeatable.

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