Semi-crystalline plastics undergo necking followed by stable drawing under tensile forces. In contrast, a rubber extends many times its original length uniformly under tension. Previously we have shown experimentally that the behavior of rubber-plastic composites in tension is intermediate between that of the rubber. Here we conduct finite element simulations of plastic-rubber-plastic trilayers laminates under tension. Using relatively simple constitutive equations for the rubber and the plastic, we examine how the composite mechanics changes as the ratio of rubber to plastic thickness is varied. We show that at small rubber thickness, the composites show necking, whereas beyond a certain rubber thickness, necking is completely eliminated.
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Necking and drawing of rubber–plastic bilayer laminates
We examine the stretching behavior of rubber–plastic composites composed of a layer of styrene–ethylene/propylene–styrene (SEPS) rubber, bonded to a layer of linear low density polyethylene (LLDPE) plastic. Dog-bone shaped samples of rubber, plastic, and rubber–plastic bilayers with rubber : plastic thickness ratio in the range of 1.2–9 were subjected to uniaxial tension tests. The degree of inhomogeneity of deformation was quantified by digital image correlation analysis of video recordings of these tests. In tension, the SEPS layer showed homogeneous deformation, whereas the LLDPE layer showed necking followed by stable drawing owing to its elastoplastic deformation behavior and post-yield strain hardening. Bilayer laminates showed behavior intermediate between the plastic and the rubber, with the degree of necking and drawing reducing as the rubber : plastic ratio increased. A simple model was developed in which the force in the bilayer was taken as the sum of forces in the plastic and the rubber layers measured independently. By applying a mechanical energy balance to this model, the changes in bilayer necking behavior with rubber thickness could be predicted qualitatively.
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- Award ID(s):
- 1636064
- NSF-PAR ID:
- 10073888
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 14
- Issue:
- 24
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 4977 to 4986
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract A continuum damage model was developed to describe the finite tensile deformation of tough double‐network (DN) hydrogels synthesized by polymerization of a water‐soluble monomer inside a highly crosslinked rigid polyelectrolyte network. Damage evolution in DN hydrogels was characterized by performing loading‐unloading tensile tests and oscillatory shear rheometry on DN hydrogels synthesized from 3‐sulfopropyl acrylate potassium salt (SAPS) and acrylamide (AAm). The model can explain all the mechanical features of finite tensile deformation of DN hydrogels, including idealized Mullins effect and permanent set observed after unloading, qualitatively and quantitatively. The constitutive equation can describe the finite elasto‐plastic tensile behavior of DN hydrogels without resorting to a yield function. It was showed that tensile mechanics of DN hydrogels in the model is controlled by two material parameters which are related to the elastic moduli of first and second networks. In effect, the ratio of these two parameters is a dimensionless number that controls the behavior of material. The model can capture the stable branch of material response during neck propagation where engineering stress becomes constant. Consistent with experimental data, by increasing the elastic modulus of the second network the finite tensile behavior of the DN hydrogel changes from necking to strain hardening.
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When subjected to the lap shear testing, spot welds created by brazing, resistance welding, or other techniques may fail either by a plug failure mode (also called pull-out mode) or an interfacial shear failure mode. In the past, plug failure mode was thought to be depend- ent on base metal ultimate tensile strength, spot diameter and plate thickness, while interfacial failure can be determined by interface shear strength and spot area. No fracture mechanics model or failure process is invoked in such an approach, and its predictive capability is often doubted compared to realistic experiments. This work conducts a parametric study to assess the failure behavior as a function of dominant three-dimensional geometric parameters based on the Gurson-Tvergaard-Needleman (GTN) damage mechanics model and no-damage mod- el respectively. Different necking conditions are considered as precursors to the two failure modes in the no-damage model. It is found out that a small ratio of spot diameter to plate thickness promotes interfacial shear failure while a large ratio favors plug failure. Other geometric parameters such as the filler interlayer thickness, if used, play a secondary role. The calculated peak force Fwt is not much different between the GTN and no-damage analyses, and better agreement is shown in the small nugget region. Normalized peak force calculated from the GTN model with the porosity f0 set to 0.01 showed the best agreement with pervious tensile shear tests on spot-welded DP980 lap joints in comparison to that calculated from the GTN model with f0 at 0.02 and the no-damage model. Note that heterogeneous distribution of materi- al strength across the joint region was considered in the GTN model, which was estimated based on the hardness map measured across the joint cross section.more » « less
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When subjected to the lap shear testing, spot welds created by brazing, resistance welding, or other techniques may fail either by a plug failure mode (also called pull-out mode) or an interfacial shear failure mode. In the past, plug failure mode was thought to be depend- ent on base metal ultimate tensile strength, spot diameter and plate thickness, while interfacial failure can be determined by interface shear strength and spot area. No fracture mechanics model or failure process is invoked in such an approach, and its predictive capability is often doubted compared to realistic experiments. This work conducts a parametric study to assess the failure behavior as a function of dominant three-dimensional geometric parameters based on the Gurson-Tvergaard-Needleman (GTN) damage mechanics model and no-damage mod- el respectively. Different necking conditions are considered as precursors to the two failure modes in the no-damage model. It is found out that a small ratio of spot diameter to plate thickness promotes interfacial shear failure while a large ratio favors plug failure. Other geometric parameters such as the filler interlayer thickness, if used, play a secondary role. The calculated peak force Fwt is not much different between the GTN and no-damage analyses, and better agreement is shown in the small nugget region. Normalized peak force calculated from the GTN model with the porosity f0 set to 0.01 showed the best agreement with pervious tensile shear tests on spot-welded DP980 lap joints in comparison to that calculated from the GTN model with f0 at 0.02 and the no-damage model. Note that heterogeneous distribution of materi- al strength across the joint region was considered in the GTN model, which was estimated based on the hardness map measured across the joint cross section.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/C8SM00684A
