Non-linear creep of polypropylene utilizing multiple integral

<p>Multiple integral representation (MIR) has been used to represent studying the effect of temperature on the amount of nonlinear creep on the semi- crystalline polypropylene (PP) under the influence of axial elastic stress. To complete this research, the Kernel functions were selected, for the purpose of performing an analogy, and for arranging the conditions for the occurrence of the first, second and third expansion in a temperature range between 20 °C-60 °C, i.e., between the glass transition and softening temperatures, within the framework of the energy law. It was observed that the independent strain time increased non-linearly with increasing stress, and non-linearly decreased with increase in temperature, although the time parameter increased non-linearly with stress and temperature directly. In general, a very satisfactory agreement between theoretical and practical results on the MIR material was observed.</p>

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A Linear Compressibility Assumption for the Multiple Integral Representation of Nonlinear Creep of Polyurethane

Journal of Applied Mechanics ◽

10.1115/1.3408525 ◽

1970 ◽

Vol 37 (2) ◽

pp. 441-448 ◽

Cited By ~ 6

Author(s):

K. G. Nolte ◽

W. N. Findley

Keyword(s):

Integral Representation ◽

Multiple Integral ◽

Kernel Functions ◽

Nonlinear Creep ◽

Volume Changes ◽

Creep Tests ◽

Third Order ◽

Nonlinear Viscoelastic ◽

Different Order ◽

Order Kernel

The assumption that volume changes associated with creep of a nonlinear viscoelastic material are only linearly dependent on the stress history is incorporated into a third-order multiple integral representation. This assumption reduces the number of independent kernel functions in the representation from 12 to 7. The traces of these independent kernels may be determined from two tension, two torsion, and one combined tension and torsion creep tests. Experiments on polyurethane are well represented by this method. The time-dependence of the kernel functions is expressed by time raised to a power with the power differing for different-order kernel functions.

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Combined Stress‐Creep Experiments on a Nonlinear Viscoelastic Material to Determine the Kernel Functions for a Multiple Integral Representation of Creep

Transactions of the Society of Rheology ◽

10.1122/1.549002 ◽

1965 ◽

Vol 9 (2) ◽

pp. 299-327 ◽

Cited By ~ 54

Author(s):

K. Onaran ◽

W. N. Findley

Keyword(s):

Integral Representation ◽

Viscoelastic Material ◽

Multiple Integral ◽

Kernel Functions ◽

Combined Stress ◽

Nonlinear Viscoelastic Material ◽

Nonlinear Viscoelastic

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Experimental Determination of Some Kernel Functions in the Multiple Integral Method for Nonlinear Creep of Polyvinyl Chloride

Journal of Applied Mechanics ◽

10.1115/1.3408763 ◽

1971 ◽

Vol 38 (1) ◽

pp. 30-38 ◽

Cited By ~ 7

Author(s):

K. Onaran ◽

W. N. Findley

Keyword(s):

Polyvinyl Chloride ◽

Viscoelastic Behavior ◽

Multiple Integral ◽

Kernel Functions ◽

Product Form ◽

Superposition Method ◽

Nonlinear Creep ◽

Nonlinear Viscoelastic ◽

Nonlinear Viscoelastic Behavior ◽

Accuracy Of Prediction

Kernel functions for mixed-time parameters in the multiple integral representation of the nonlinear viscoelastic behavior of polyvinyl chloride were determined from both two-step tension and two-step torsion creep experiments. First and second-order terms were used for tension and first and third-order terms were used for torsion to describe these kernel functions. Stepdown tests were needed for good accuracy of representation. Accuracy of prediction was good for stepdown but not stepup tests. The product form assumption for these kernel functions and the modified superposition method were also investigated. The latter gave the best overall predictability of the three methods, although the product form was nearly as satisfactory.

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Buckling and vibration analysis of shape memory laminated composite beams under axially heterogeneous in-plane loads in the glass transition temperature region

SN Applied Sciences ◽

10.1007/s42452-021-04438-2 ◽

2021 ◽

Vol 3 (4) ◽

Author(s):

Nilesh Tiwari ◽

A. A. Shaikh

Keyword(s):

Glass Transition ◽

Transition Temperature ◽

Glass Transition Temperature ◽

Boundary Conditions ◽

Shape Memory ◽

Transition Region ◽

Shape Memory Polymer ◽

Shear Deformation Theory ◽

Effect Of Temperature ◽

Glass Transition Region

AbstractBuckling and vibration study of the shape memory polymer composites (SMPC) across the glass transition temperature under heterogeneous loading conditions are presented. Finite element analysis based on C° continuity equation through the higher order shear deformation theory (HSDT) is employed considering non linear Von Karman approach to estimate critical buckling and vibration for the temperature span from 273 to 373 K. Extensive numerical investigations are presented to understand the effect of temperature, boundary conditions, aspect ratio, fiber orientations, laminate stacking and modes of phenomenon on the buckling and vibration behavior of SMPC beam along with the validation and convergence study. Effect of thermal conditions, particularly in the glass transition region of the shape memory polymer, is considerable and presents cohesive relation between dynamic modulus properties with magnitude of critical buckling and vibration. Moreover, it has also been inferred that type of axial loading condition along with the corresponding boundary conditions significantly affect the buckling and vibration load across the glass transition region.

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Nonlinear creep in a steel-reinforced concrete beam

Вестник гражданских инженеров ◽

10.23968/1999-5571-2020-17-5-108-116 ◽

2020 ◽

Vol 17 (5) ◽

pp. 108-116

Author(s):

S. O. Chepilko ◽

Keyword(s):

Reinforced Concrete ◽

Concrete Beam ◽

Reinforced Concrete Beam ◽

Reinforced Concrete Beams ◽

Nonlinear Creep ◽

Short Term ◽

Nonlinear Integral Equations ◽

Steel Reinforced Concrete ◽

Linear Creep ◽

Resolving System

Problems of taking into account nonlinear creep in steel- reinforced concrete beams are considered basing on the integral equation of viscous-elastic-plasticity of concrete. There has been obtained the resolving system of nonlinear integral equations, a linearization of this system has been carried out, its asymptotic solutions have been written out for the theory of elastic heredity case. The analysis of taking into account nonlinear creep has been performed compared with the linear creep equations and an instantaneous (short-term) loading allowing for concrete’s nonlinear diagram.

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Effect of temperature on damage mechanisms and mechanical behaviour of an acrylic-thermoplastic-matrix and glass-fibre-reinforced composite

Journal of Composite Materials ◽

10.1177/0021998320929056 ◽

2020 ◽

Vol 54 (27) ◽

pp. 4269-4282

Author(s):

E Boissin ◽

C Bois ◽

J-C Wahl ◽

T Palin-Luc

Keyword(s):

Glass Transition ◽

Transition Temperature ◽

Polymer Matrix ◽

Mechanical Response ◽

Polymer Matrix Composites ◽

Effect Of Temperature ◽

Matrix Composites ◽

Service Temperature ◽

Damage Mechanisms ◽

Temperature Range

The mechanical response of polymer matrix composites exhibits a temperature dependency even if the service temperature range is lower than the glass transition temperature of the polymer matrix. This dependency is mainly due to the temperature effect on the mechanical behaviour of the polymer matrix. However, the micro- and meso-structures driving the composite anisotropy and local stress distribution play an essential role regarding the effect of temperature on damage mechanisms specific to reinforced polymers. There are few data in the literature on the sensitivity to temperature of damage mechanisms and scenarios of polymer matrix composites regardless of loading type. In this paper, after a synthetic literature review of the effect of temperature on polymers and polymer composites, several complementary tests are proposed to analyse the temperature effect on damage mechanisms undergone by laminated composites under in-plane quasi static loadings. These tests are applied to an acrylic-thermoplastic composite reinforced by glass fibres in its service temperature range of –20℃ to 60℃. The results show that the testing temperature has a significant impact on the mechanical response and damage mechanisms of the composite material in the selected temperature range, which is markedly lower than the glass transition temperature (around 100℃). While the temperature rise generates a gradual decrease in matrix stiffness and strength, the increase in matrix ductility associated to the stress heterogeneity in the composite microstructure produces a rise in the transverse cracking threshold and removes this damage mode during quasi-static tensile tests when the temperature shifts from 15℃ to 40℃.

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Concerning a Creep Surface Derived From a Multiple Integral Representation for 304 Stainless Steel Under Combined Tension and Torsion

Journal of Applied Mechanics ◽

10.1115/1.3424417 ◽

1978 ◽

Vol 45 (4) ◽

pp. 773-779 ◽

Cited By ~ 4

Author(s):

R. Mark ◽

W. N. Findley

Keyword(s):

Stainless Steel ◽

Creep Rate ◽

Integral Representation ◽

Power Function ◽

Multiple Integral ◽

304 Stainless Steel ◽

Creep Data ◽

Creep Tests ◽

Third Order ◽

Good Agreement

It is shown that a creep surface, defined in terms of a prescribed creep rate, can be determined from the multiple integral formulation representing the creep data. The creep surface for 304 stainless steel was found to be in good agreement with a Mises ellipse. Observed creep rate vectors for this alloy were found to be normal to a Mises ellipse. These results were obtained from creep tests performed on 304 stainless steel under combined tension and torsion at 593°C (1100°F). Creep strains observed for at least 100 hr were adequately represented by a power function of time, the exponent of which was independent of stress. A third-order multiple integral representation together with a limiting stress below which creep does not occur was employed to describe satisfactorily the constant stress creep data.

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Effect of Temperature and Pressure on Segmental Relaxation in Polymethylphenylsiloxane

Rubber Chemistry and Technology ◽

10.5254/1.3547790 ◽

2003 ◽

Vol 76 (5) ◽

pp. 1106-1115 ◽

Cited By ~ 12

Author(s):

S. Pawlus ◽

S. J. Rzoska ◽

J. Ziolo ◽

M. Paluch ◽

C. M. Roland

Keyword(s):

Molecular Weight ◽

Glass Transition ◽

Pressure Dependence ◽

Activation Volume ◽

Relaxation Times ◽

Effect Of Temperature ◽

Loss Peak ◽

Glass Transition Temperatures ◽

Segmental Relaxation ◽

Temperature And Pressure

Abstract Segmental relaxation in a series of polymethylphenylsiloxanes (PMPS) was studied using dielectric spectroscopy. The measurements covered a temperature range of more than 40 deg at pressures from ambient to 115 MPa. The results confirmed that the shape of the loss peak is independent of temperature, pressure and molecular weight. Consequently, the Tg -scaled dependence of the relaxation times was also independent of molecular weight. The pressure dependence of the relaxation times was characterized by means of the activation volume. This quantity changes markedly with pressure at a given temperature. However, the activation volume at the respective glass transition temperatures of the PMPS are essentially invariant to molecular weight. Finally, we measured the dependence of Tg on pressure, with the results well-described by the Andersson equation.

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Effect of Manufacturing Process Parameters on Property Evolution of Printed Circuit Board Laminates

Volume 9: Micro- and Nano-Systems Engineering and Packaging, Parts A and B ◽

10.1115/imece2012-93057 ◽

2012 ◽

Author(s):

Pradeep Lall ◽

Vikalp Narayan ◽

Jim Blanche ◽

Mark Strickland

Keyword(s):

Glass Transition ◽

Transition Temperature ◽

Glass Transition Temperature ◽

Manufacturing Process ◽

Printed Circuit Board ◽

Statistical Significance ◽

Circuit Board ◽

Effect Of Temperature ◽

Process Variables ◽

Printed Circuit

The effect of temperature exposure encountered both during assembly and in fielded products, has a known influence on glass transition temperature of printed-circuit board (PCB) laminate materials. Printed circuit board laminates such as FR4 are composites of epoxy resin with woven fiberglass reinforcement. Interaction between manufacturing process variables that impact the changes in glass transition temperature (Tg) has been studied. The laminates studied have been broadly classified into high-Tg, and mid-Tg laminates. Different sets of reflow profiles were created by varying the process variables including, time above liquidus, peak temperature, ramp rate and cooling rate. The effect of multiple reflows encountered in normal assembly or board re-work has been studied by exposing the assemblies to multiple reflows between 2x–6x. Changes to the glass transition temperature have been classified by measurement of the glass transition temperature were measured via Thermo Mechanical Analysis (TMA). Statistical analysis of the variables has been used to determine the statistical significance of the measured changes for large populations.

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