An approach based on mechanical testing and finite element modeling is presented to establish the stress strain relationship for polymers when necking evolves under tension . The paper gives details of criteria used for evaluating the stress strain relationship during the necking process and depicts how the total strain range is divided into several sections for the ease of the iterative calculation process . High density polyethylene is used as a sample polymer to illustrate the approach . The results show that this approach can consider non linear and creep deformation during the neck evolvement and the stress strain relationship established can be applied to a finite element model to regenerate force elongation curve and cross section reduction measured from the mechanical testing . Polymers such as high density polyethylene are susceptible to spontaneous strain localization and strain hardening that arises from structural rejuvenation induced by large deformation . In view that the ability to predict necking in polymers is essential for assurance of their reliable performance especially when considering applications such as pipelines and pressure vessels understanding such deformation behavior is of utmost importance . As a result much of the research work on polymers has been dedicated to study of the necking behavior and the damage evolution process during the neck development . However challenges are encountered due to the time dependent deformation process that plays a critical role for many polymers in long term service . As a result most of the characterization methods to evaluate reliability of the long term performance of polymers require tests on full sized products . Since those tests are time consuming to carry out and involve significant uncertainty in its prediction accuracy some researchers have considered a different approach that is to evaluate the performance through numerical simulation for which the first step is to establish the stress strain relationship for the deformation process . During the last few decades many approaches have been proposed to establish the stress strain relationship for polymer deformation . Some of those approaches often known as slip link or tube models are an extension from classical rubber elasticity to consider chain entanglements in the molecular network for the mechanical response during the deformation . One of those approaches commonly known as Edward Vilgis theory separates number of permanent joints from number of topological constraints in the expression of free energy as a function of stretch ratio . Based on this model formation of cross links in radiated polyethylene was investigated and found to increase the effective chain entanglements during the deformation . Other approaches consider interactions at the molecular level to relate the molecular interactions with the macroscopic deformation behavior . One of the first models in those approaches took into account rotation and alignment of molecular chain segments for establishing the stress strain relationship for large deformation in amorphous polymers . The model was later extended to three dimensional deformation . More recently Wu and Buckley developed a model based on molecular interaction to capture. 


Highlights:
Testing and FEM were used to establish the constitutive equation for necking in polymers. Creep is included in the constitutive equation in order to regenerate the necking behavior. Constitutive equation is established for HDPE in two specimen geometries at two cross head speeds.