Microscopic Mechanisms of Strain Hardening in Glassy Polymers

The mechanisms underlying the increase in stress for large mechanical strains of a polymer glass, quantified by the strain-hardening modulus, are still poorly understood. In the present paper we aim to elucidate this matter and present new mechanisms. Molecular-dynamics simulations of two polymers with very different strain-hardening moduli (polycarbonate and polystyrene) have been carried out. Nonaffine displacements occur because of steric hindrances and connectivity constraints. We argue that it is not necessary to introduce the concept of entanglements to understand strain hardening, but that hardening is rather coupled with the increase in the rate of nonaffine particle displacements. This rate increases faster for polycarbonate, which has the higher strain-hardening modulus. Also more nonaffine chain stretching is present for polycarbonate. It is shown that the inner distances of such a nonaffinely deformed chain can be well described by the inner distances of the worm-like chain, but with an effective stiffness length (equal to the Kuhn length for an infinite worm-like chain) that increases during deformation. It originates from the finite extensibility of the chain. In this way the increase in nonaffine particle displacement can be understood as resulting from an increase in the effective stiffness length of the perturbed chain during deformation, so that at larger strains a higher rate of plastic events in terms of nonaffine displacement is necessary, causing in turn the observed strain hardening in polymer glasses.

Deforming glassy polystyrene: Influence of pressure, thermal history, and deformation mode on yielding and hardening

The toughness of a polymer glass is determined by the interplay of yielding, strain softening, and strain hardening. Molecular-dynamics simulations of a typical polymer glass, atactic polystyrene, under the influence of active deformation have been carried out to enlighten these processes. It is observed that the dominant interaction for the yield peak is of interchain nature and for the strain hardening of intrachain nature. A connection is made with the microscopic cage-to-cage motion. It is found that the deformation does not lead to complete erasure of the thermal history but that differences persist at large length scales. Also we find that the strain-hardening modulus increases with increasing external pressure. This new observation cannot be explained by current theories such as the one based on the entanglement picture and the inclusion of this effect will lead to an improvement in constitutive modeling.

Comparison of small and large deformation rheological properties of wheat dough and gluten

The rheological properties of dough and gluten are important for end-use quality of flour but there is a lack of knowledge of the relationships between fundamental and empirical tests and how they relate to flour composition and gluten quality. Dough and gluten from six breadmaking wheat qualities were subjected to a range of rheological tests. Fundamental (small-deformation) rheological characterizations (dynamic oscillatory shear and creep recovery) were performed on gluten to avoid the nonlinear influence of the starch component, whereas large deformation tests were conducted on both dough and gluten. A number of variables from the various curves were considered and subjected to a principal component analysis (PCA) to get an overview of relationships between the various variables. The first component represented variability in protein quality, associated with elasticity and tenacity in large deformation (large positive loadings for resistance to extension and initial slope of dough and gluten extension curves recorded by the SMS/Kieffer dough and gluten extensibility rig, and the tenacity and strain hardening index of dough measured by the Dobraszczyk/Roberts dough inflation system), the elastic character of the hydrated gluten proteins (large positive loading for elastic modulus [G'], large negative loadings for tan delta and steady state compliance [J(e)(0)]), the presence of high molecular weight glutenin subunits (HMW-GS) 5+10 vs. 2+12, and a size distribution of glutenin polymers shifted toward the high-end range. The second principal component was associated with flour protein content. Certain rheological data were influenced by protein content in addition to protein quality (area under dough extension curves and dough inflation curves [W]). The approach made it possible to bridge the gap between fundamental rheological properties, empirical measurements of physical properties, protein composition, and size distribution. The interpretation of this study gave indications of the molecular basis for differences in breadmaking performance.

Wheat protein quality in relation to baking performance evaluated by the Chorleywood bread process and a hearth bread baking test

The relationships between wheat protein quality and baking properties of 20 flour samples were studied for two breadmaking processes; a hearth bread test and the Chorleywood Bread Process (CBP). The strain hardening index obtained from dough inflation measurements, the proportion of unextractable polymeric protein, and mixing properties were among the variables found to be good indicators of protein quality and suitable for predicting potential baking quality of wheat flours. By partial least squares regression, flour and dough test variables were able to account for 71-93% of the variation in crumb texture, form ratio and volume of hearth loaves made using optimal mixing and fixed proving times. These protein quality variables were, however, not related to the volume of loaves produced by the CBP using mixing to constant work input and proving to constant height. On the other hand, variation in crumb texture of CBP loaves (54-55%) could be explained by protein quality. The results underline that the choice of baking procedure and loaf characteristics is vital in assessing the protein quality of flours. (C) 2003 Elsevier Ltd. All rights reserved.

Extensional rheology and stability of gas cell walls in bread doughs at elevated temperatures in relation to breadmaking performance

The rheological properties of gas cell walls in bread doughs are considered to be important in relation to their stability and gas retention during proof and baking. Large deformation rheological properties of gas cell walls were measured using biaxial extension for a number of doughs of varying breadmaking quality at constant strain rate and elevated temperatures of 25-60degreesC. Strain hardening and failure strain of cell walls both decreased with temperature, with cell walls in good breadmaking doughs remaining stable and retaining their strain hardening properties at higher temperatures (60degreesC), while the cell walls of poor breadmaking doughs became unstable at lower temperatures (45-50degreesC) and had lower strain hardening. Strain hardening measured at 50degreesC gave good correlations with baking volume, with the best correlations achieved between rheological measurements and baking tests that used similar mixing conditions. As predicted by the considered failure criterion, a strain hardening value of I defines a region below which gas cell walls become unstable, and discriminates well between the baking quality of a range of commercial flour blends of varying quality. This indicates that the stability of gas cell walls during baking is strongly related to strain hardening properties, and that extensional rheological measurements can be used as indicators of baking quality.

Comparison of predictions of baking volume using large deformation rheological properties

Three large deformation rheological tests, the Kieffer dough extensibility system, the D/R dough inflation system and the 2 g mixograph test, were carried out on doughs made from a large number of winter wheat lines and cultivars grown in Poland. These lines and cultivars represented a broad spread in baking performance in order to assess their suitability as predictors of baking volume. The parameters most closely associated with baking volume were strain hardening index, bubble failure strain, and mixograph bandwidth at 10min. Simple correlations with baking volume indicate that bubble failure strain and strain hardening index give the highest correlations, whilst the use of best subsets regression, which selects the best combination of parameters, gave increased correlations with R-2 = 0.865 for dough inflation parameters, R-2 = 0. 842 for Kieffer parameters and R-2 = 0.760 for mixograph parameters. (c) 2007 Elsevier Ltd. All rights reserved.

Rheology and the breadmaking process

The applications of rheology to the main processes encountered during breadmaking (mixing, sheeting, fermentation and baking) are reviewed. The most commonly used rheological test methods and their relationships to product functionality are reviewed. It is shown that the most commonly used method for rheological testing of doughs, shear oscillation dynamic rheology, is generally used under deformation conditions inappropriate for breadmaking and shows little relationship with end-use performance. The frequency range used in conventional shear oscillation tests is limited to the plateau region, which is insensitive to changes in the HMW glutenin polymers thought to be responsible for variations in baking quality. The appropriate deformation conditions can be accessed either by long-time creep or relaxation measurements, or by large deformation extensional measurements at low strain rates and elevated temperatures. Molecular size and structure of the gluten polymers that make up the major structural components of wheat are related to their rheological properties via modern polymer rheology concepts. Interactions between polymer chain entanglements and branching are seen to be the key mechanisms determining the rheology of HMW polymers. Recent work confirms the observation that the dynamic shear plateau modulus is essentially independent of variations in MW of glutens amongst wheat varieties of varying baking performance and also that it is not the size of the soluble glutenin polymers, but the secondary structural and rheological properties of the insoluble polymer fraction that are mainly responsible for variations in baking performance. Extensional strain hardening has been shown to be a sensitive indicator of entanglements and long-chain branching in HMW polymers, and is well related to baking performance of bread doughs. The Considere failure criterion for instability in extension of polymers defines a region below which bubble walls become unstable, and predicts that when strain hardening falls below a value of around 1, bubble walls are no longer stable and coalesce rapidly, resulting in loss of gas retention and lower volume and texture. Strain hardening in doughs has been shown to reach this value at increasingly higher temperatures for better breadmaking varieties and is directly related to bubble stability and baking performance. (C) 2003 Elsevier Ltd. All rights reserved.

The physics of baking: rheological and polymer molecular structure-function relationships in breadmaking

Molecular size and structure of the gluten polymers that make up the major structural components of wheat are related to their rheological properties via modem polymer rheology concepts. Interactions between polymer chain entanglements and branching are seen to be the key mechanisms determining the rheology of HMW polymers. Recent work confirms the observation that dynamic shear plateau modulus is essentially independent of variations in MW amongst wheat varieties of varying baking performance and is not related to variations in baking performance, and that it is not the size of the soluble glutenin polymers, but the structural and rheological properties of the insoluble polymer fraction that are mainly responsible for variations in baking performance. The rheological properties of gas cell walls in bread doughs are considered to be important in relation to their stability and gas retention during proof and baking, in particular their extensional strain hardening properties. Large deformation rheological properties of gas cell walls were measured using biaxial extension for a number of doughs of varying breadmaking quality at constant strain rate and elevated temperatures in the range 25-60 degrees C. Strain hardening and failure strain of cell walls were both seen to decrease with temperature, with cell walls in good breadmaking doughs remaining stable and retaining their strain hardening properties to higher temperatures (60 degrees C), whilst the cell walls of poor breadmaking doughs became unstable at lower temperatures (45-50 degrees C) and had lower strain hardening. Strain hardening measured at 50 degrees C gave good correlations with baking volume, with the best correlations achieved between those rheological measurements and baking tests which used similar mixing conditions. As predicted by the Considere failure criterion, a strain hardening value of I defines a region below which gas cell walls become unstable, and discriminates well between the baking quality of a range of commercial flour blends of varying quality. This indicates that the stability of gas cell walls during baking is strongly related to their strain hardening properties, and that extensional rheological measurements can be used as predictors of baking quality. (C) 2004 Elsevier B.V. All rights reserved.

The physics of baking: rheological and polymer molecular structure-function relationships in breadmaking

Molecular size and structure of the gluten polymers that make up the major structural components of wheat are related to their rheological properties via modern polymer rheology concepts. Interactions between polymer chain entanglements and branching are seen to be the key mechanisms determining the rheology of HMW polymers. Recent work confirms the observation that dynamic shear plateau modulus is essentially independent of variations in MW amongst wheat varieties of varying baking performance and is not related to variations in baking performance, and that it is not the size of the soluble glutenin polymers, but the structural and rheological properties of the insoluble polymer fraction that are mainly responsible for variations in baking performance. The rheological properties of gas cell walls in bread doughs are considered to be important in relation to their stability and gas retention during proof and baking, in particular their extensional strain hardening properties. Large deformation rheological properties of gas cell walls were measured using biaxial extension for a number of doughs of varying breadmaking quality at constant strain rate and elevated temperatures in the range 25oC to 60oC. Strain hardening and failure strain of cell walls were both seen to decrease with temperature, with cell walls in good breadmaking doughs remaining stable and retaining their strain hardening properties to higher temperatures (60oC), whilst the cell walls of poor breadmaking doughs became unstable at lower temperatures (45oC to 50oC) and had lower strain hardening. Strain hardening measured at 50oC gave good correlations with baking volume, with the best correlations achieved between those rheological measurements and baking tests which used similar mixing conditions. As predicted by the Considere failure criterion, a strain hardening value of 1 defines a region below which gas cell walls become unstable, and discriminates well between the baking quality of a range of commercial flour blends of varying quality. This indicates that the stability of gas cell walls during baking is strongly related to their strain hardening properties, and that extensional rheological measurements can be used as predictors of baking quality.

Damage rate is a predictor of fatigue life and creep strain rate in fatigue of tensile human cortical bone samples

We present results on the growth of damage in 29 fatigue tests of human femoral cortical bone from four individuals, aged 53–79. In these tests we examine the interdependency of stress, cycles to failure, rate of creep strain, and rate of modulus loss. The behavior of creep rates has been reported recently for the same donors as an effect of stress and cycles (Cotton, J. R., Zioupos, P., Winwood, K., and Taylor, M., 2003, "Analysis of Creep Strain During Tensile Fatigue of Cortical Bone," J. Biomech. 36, pp. 943–949). In the present paper we first examine how the evolution of damage (drop in modulus per cycle) is associated with the stress level or the "normalized stress" level (stress divided by specimen modulus), and results show the rate of modulus loss fits better as a function of normalized stress. However, we find here that even better correlations can be established between either the cycles to failure or creep rates versus rates of damage than any of these three measures versus normalized stress. The data indicate that damage rates can be excellent predictors of fatigue life and creep strain rates in tensile fatigue of human cortical bone for use in practical problems and computer simulations.