Onset Of Strain Hardening Research Articles

Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution.

The transient elongational viscosity ηe(t) of the polymer melt is known to exhibit strain hardening, which depends on the strain rate ε˙. This phenomenon was elucidated by the difference of chain stretching in the entanglement network between extension and shear. However, to date, the microscopic evolution of polymer melt has not been fully statistically analyzed. In this work, the radial size distributions P(Rg,t) of linear polymers are explored by dissipative particle dynamics during the stretching processes. In uniaxial extensional flow, it is observed that the mean radius of gyration R¯g(t) and standard deviation σ(t) remain unchanged until the onset of strain hardening, corresponding to linear viscoelasticity. Both R¯g and σ rise rapidly in the non-linear regime, and bimodal size distribution can emerge. Moreover, the onset of strain hardening is found to be insensitive to the Hencky strain (ε˙Ht) and chain length (N).

Evaluation of microscopic structural changes during strain hardening of polyethylene solids using In situ Raman, SAXS, and WAXD measurements under step-cycle test

We have examined the mechanism of strain hardening of polyethylene (PE) using a step-cycle test with in situ Raman spectroscopy, small-angle X-ray scattering, and wide-angle X-ray diffraction measurements. A stable fibrillar structure was formed at the onset of strain hardening. The fraction of the long-consecutive trans chains increased and decreased with increasing and decreasing strain during the stretching and unloading steps, respectively. The peak shift of the C–C stretching mode showed a red shift by applying the stretching stress to the specimen, accompanied by the broadening of the peak width. The broadening of the Raman band is interpreted as the strong stretching load becoming concentrated on the taut-tie chains. According to these results, we concluded that the strain hardening was caused by the increment of the modulus resulting from the increase in the number of taut-tie chains caused by chain pull-out from the crystalline structure. ・ Strain hardening of PE was investigated via various measurements. ・ The strain-hardening behavior was dominated by plastic deformation. ・ Increasing the amount of taut-tie chains dominates the strain-hardening modulus.

Stress-strain curves for hot-rolled steels

The use of advanced analytical and numerical modelling in structural engineering has increased rapidly in recent years. A key feature of these models is an accurate description of the material stress-strain behaviour. Development of standardised constitutive equations for the full engineering stress-strain response of hot-rolled carbon steels is the subject of the present paper. The proposed models, which offer different options for the representation of the strain hardening region, feature an elastic response up to the yield point, followed by a yield plateau and strain hardening up to the ultimate tensile stress. The Young's modulus E, the yield stress fy and the ultimate stress fu are generally readily available to the engineer, but other key parameters, including the strains at the onset of strain hardening and at the ultimate stress, are not, and hence require predictive expressions. These expressions have been developed herein and calibrated against material stress-strain data collected from the literature. Unlike the widely used ECCS model, which has a constant strain hardening slope, the proposed models, reflecting the collected test data, have a yield plateau length and strain hardening characteristics which vary with the ratio of yield to ultimate stress (i.e. with material grade). The proposed models require three basic input parameters (E, fy and fu), are simple to implement in analytical or numerical models, and are shown herein to be more accurate than the widely employed ECCS model. The proposed models are based on and hence representative of modern hot-rolled steels from around the world.

Using the Hollomon Model to Predict Strain-Hardening in Metals

Stress – strain values obtained from tensile tests of aluminium and steel is used to evaluate the true stress – true strain values. The Hollomon’s model is then used to predict the strain-hardening behavior in the two specimens. It is clearly seen that the strain-hardening behavior in metals can be described using the Hollomon’s model. However, we have assumed that the onset of strain-hardening is at the yield point up until the ultimate tensile strength. The correlation between the experimental true stress – true strain values of aluminium and the calculated values using the Hollomon equation is much better than that of steel.

Time-Dependent Mechanochemical Response of SP-Cross-Linked PMMA

Time-dependent mechanochemical activation of spiropyran (SP) mechanophores in cross-linked PMMA under creep loading is examined. In contrast to monotonic torsion (constant strain rate) results, the desired force-induced electrocyclic ring-opening of SP to the fluorescent merocyanine (MC) form is achieved at creep stress levels less than the yield stress of the bulk polymer. Lower values of stress require longer time, but much smaller strains for initiation of activation. Additionally, the first measurable detection of the reaction corresponds closely to the maximum creep strain rate, revealing mechanophore activation occurs near the onset of strain hardening, when polymer mobility is highest. The strong correlation between mechanical activation of the spiropyran and the rate of deformation suggests the potential for SP mechanophores as molecular probes of polymer relaxation and flow.

A nonaffine network model for elastomers undergoing finite deformations

In this work, we construct a new physics-based model of rubber elasticity to capture the strain softening, strain hardening, and deformation-state dependent response of rubber materials undergoing finite deformations. This model is unique in its ability to capture large-stretch mechanical behavior with parameters that are connected to the polymer chemistry and can also be easily identified with the important characteristics of the macroscopic stress–stretch response. The microscopic picture consists of two components: a crosslinked network of Langevin chains and an entangled network with chains confined to a nonaffine tube. These represent, respectively, changes in entropy due to thermally averaged chain conformations and changes in entropy due to the magnitude of these conformational fluctuations. A simple analytical form for the strain energy density is obtained using Rubinstein and Panyukov's single-chain description of network behavior. The model only depends on three parameters that together define the initial modulus, extent of strain softening, and the onset of strain hardening. Fits to large stretch data for natural rubber, silicone rubber, VHB 4905 (polyacrylate rubber), and b186 rubber (a carbon black-filled rubber) are presented, and a comparison is made with other similar constitutive models of large-stretch rubber elasticity. We demonstrate that the proposed model provides a complete description of elastomers undergoing large deformations for different applied loading configurations. Moreover, since the strain energy is obtained using a clear set of physical assumptions, this model may be tested and used to interpret the results of computer simulation and experiments on polymers of known microscopic structure.

Uniaxial extensional rheology of well-characterized comb polymers

We present a detailed systematic investigation of the transient uniaxial extensional response of a series of well-characterized, anionically synthesized comb polystyrenes and polyisoprenes. The comb architecture consists of a linear chain backbone with multiple branches of equal molar mass, and represents an excellent model branched polymer. The linear viscoelastic response has been studied already in great detail. Our results indicate that the strain hardening becomes more important as the Hencky strain rate is increased. In general, the larger the number of entanglements of the segments between branches and/or of the branches, the stronger the strain hardening and the smaller the characteristic rate for its onset. The key molecular parameter appears to be the number of entanglements per branch. By varying it, one can tailor the amount and onset of strain hardening. This can be rationalized by accounting for the combined effect of backbone tube dilation and extra friction, brought about by the branches. In fact, we define an effective “stretch time” of the comb as the timescale for stretch relaxation along the dilated backbone tube when accounting for the large friction that comes from the branches and suggest that extension hardening occurs at rates equal to or greater than its inverse. The good comparison of this prediction to experimental data is a promising guide toward a universal framework for understanding the effects of branches on extensional rheology, and hence providing some insight into the behavior of long-chain branched polyolefins.

Real time mechano-optical study on deformation behavior of PTMO/CHDI-based polyetherurethanes under uniaxial extension

Real time mechano-optical properties of two homologous segmented, thermoplastic polyurethanes (TPUs) obtained from the stoichiometric reactions of trans-1,4-cyclohexyl diisocyanate (CHDI) and poly(tetramethylene oxide)glycol (PTMO) were investigated. PTMO oligomers used had number average molecular weights 〈Mn〉 of 1020 and 2040 g/mol, resulting in TPUs with urethane hard segment contents of 14 and 7.5% by weight. AFM studies showed intertwined microphase morphology. Stress–strain measurements demonstrated the formation of very strong, elastomeric materials, with ultimate tensile strengths of 23–25 MPa and elongation at break values of about 1000%. Mechano-optical behavior of these polymers exhibited multiple regime behavior. The first strain optical regime is linear where primarily the soft segments orient. The transition between the first and second strain optical regimes was found to correspond to the saturation of straining of the soft segments that lead to start of rotation of hard segments in the stretching direction. The start of Regime II coincides with the onset of strain hardening and the distance between the hard segments increases appreciably with stretching in this regime. Increasing the soft segment length was found to promote its strain-induced crystallization.

Stages of Structural Ordering Leading to Stress Induced Crystallization of PEEK Films: A Mechano-Optical Study on Deformation, Relaxation and Retraction

Influence of rubbery state large uniaxial deformation followed by relaxation and retraction stages on the mechano-optical behavior of cast amorphous poly(ether ether ketone) films was investigated. At early stage of stretching the birefringence remains linearly proportional to stress. In this linear optical regime, the material remains amorphous. Beyond a critical stress level, a deviation from linearity is observed where a small fraction of the material exhibit extreme preferred orientation with substantial translational disorder resembling nematic-like order. The onset of this deviation also coincides with the onset of strain hardening. Stretching beyond this transition leads to stress induced crystallization. Films stretched to deformation levels well below the onset of strain hardening, remain amorphous before and after the relaxation stages. The entropy reduction gained through deformation of the polymer chains is not sufficient to form crystalline order at short time scales. Once the initial deformation increased beyond the onset of strain hardening, a long-range network of connected crystallites establishes itself.

Mechanical properties of cellulose fibres and wood. Orientational aspectsin situinvestigated with synchrotron radiation

Highly oriented native cellulose fibres (flax) and softwood (pine) have been investigated by means of X-ray diffraction. Local structural information was obtained by using X-ray microbeams. Tensile tests were performed in situ, revealing a change of orientation of cellulose microfibrils in materials with tensile strain. In flax fibres, the microfibrils rotate during the first percent of stretching, into a more parallel orientation with respect to the fibre axis. For wood, a decrease of orientation with the onset of strain hardening is found for the first time.

Nonlinear Dynamics of Confined Polymer Melts with Attractive Walls

A scaling model is presented to analyze the reversible strain-hardening phenomenon in end-tethered polymer clay nanocomposites (Krishnamoorti, R.; Giannelis, E. P. Langmuir 2001, 17, 1448). It is assumed that for attractive clay-polymer interactions a fraction of the polymer chains that span the space between opposite clay plates get adsorbed on them, thereby bridging the plates. Under large amplitude oscillatory shear, such bridges are stretched, and this results in the strain-hardening behavior. The onset of strain hardening is predicted to be dependent only on the average distance separating the two plates and is independent of the frequency of the oscillations and the polymer molecular weight.

Hardening by Crystallization During Superplastic Flow in a Powder-metallurgy-processed Zr65Al10Ni10Cu15 Glass Metallic Alloy

The superplastic behavior of the Zr65Al10Ni10Cu15 glass metallic alloy produced by the powder metallurgy method was examined in the supercooled liquid region. A tensile elongation as large as 750% was obtained at 6.3 × 10−3 s−1 at 697 K. Large strain hardening took place during the course of deformation and systematic trend was observed in the hardening behavior. Plots of stress versus strain and strain rate versus stress at 697 K showed that Newtonian viscous flow governed the plastic flow until the onset of strain hardening. Microstructure and differential scanning calorimetry analyses as well as flow stress versus testing time curves provided consistent evidence that the strain hardening was induced by crystallization. Crystallization was enhanced in the gauge region (deformed region) as compared to the grip region (undeformed region). Crystallization is expected to decrease tensile ductility by decreasing the strain-rate-sensitivity value and increasing the degree of brittleness. Hardening by crystallization, however, can contribute to neck stability if crystallization is enhanced in the neck region. The strain hardening and plastic stability parameters were measured as a function of strain for different strain rates at 696 K. The strain hardening parameter remained highly positive until failure. Because of this, the neck stability parameter (I) could be I < 0 in the entire hardening region. The contribution of hardening by crystallization to neck stability was found to be much more significant than that by grain growth in the superplastic metallic alloys. Reducing the specimen heating-and-holding time was suggested to promote superplasticity deformation without delaying initiation of crystallization. The largest tensile strain in the hardening region where crystallization may be obtained at the strain rates and temperatures where crystallization rate is controlled to be the lowest while maintaining I ≤ 0 throughout deformation.

Resistance to uniaxial extensional flow of fibre suspensions

The tensile stress due to resistance to uniaxial extensional flow of fibre suspensions in Newtonian and non-Newtonian fluids has been measured using the filament stretching technique. It has been found that addition of fibres to a Newtonian fluid increases the extensional viscosity. The steady state results agree with Bachelor’s theory and the stress growth behaviour is qualitatively predicted by the theory of Dinh and Armstrong. Experimental results from this work have also shown that the behaviour of a fibre suspension in viscoelastic fluid is qualitatively described by Fan’s equation. The added fibres increase the extensional stress growth coefficient of the viscoelastic fluid at low strain but have marginal effect on the fluid after the onset of strain-hardening.

Change of modulus and yielding properties of syndiotactic polypropylene with the glass transition

AbstractSemi-crystalline polymers like syndiotactic polypropylene pass during tensile deformation different stages with cross-overs at four critical points. Temperature variation above ambient changes the stresses at the critical points, but leaves the strains constant. Cooling down to the glass transition leads to the following changes: Fracture occurs before the onset of strain hardening. Yield point strain shifts to lower values. Young’s modulus increases by a factor on the order of the inverse of the crystallinity, as can be expected when the amorphous regions also contribute to the transmission of forces.

Kinetics of rapid structural changes during heat setting of preoriented PEEK/PEI blend films as followed by spectral birefringence technique

The influence of composition and preorientation on the development of structural hierarchy during heat setting of PEEK/PEI films was investigated using on-line birefringence, and off-line wide-angle and small-angle X-ray scattering, infrared dichroism and thermal analysis techniques. When the PEEK/PEI blends are drawn to deformation levels below the onset of strain hardening, the subsequent heat setting at high temperature starts with a large relaxation process followed by a fast crystallization and a long-term slow structural rearrangement stages. When the films are predrawn beyond a critical structural level (crystallinity and orientation), the initial relaxation stage disappears. This signifies that beyond a critical structural order a long-range physical network, where the nodes consist of crystallized domains and chain—self and cross-entanglements—are formed. This physical network allows the entropy driven shrinkage stresses to be maintained that results in the development of oriented crystalline phase. The addition of non-crystallizable PEI chains was found to retard the formation of this ‘network structure’ resulting in lower orientation levels.

Crazing Micromechanism in Glassy Atactic Polystyrene and Its Blends with Poly(2,6-dimethyl-1,4-diphenyl oxides) by AFM

Crazing in glassy polymer thin films was found to follow a micronecking process similar to that of local shear deformation in ductile polymers. The void fraction in the fully necked craze region was determined, and a close-packed fibril structure was concluded. The local stress and strain within the craze were obtained from AFM topographic data by the Bridgman's plasticity analysis. The stress/strain curve of craze fibrillation was subsequently determined where an apparent strain softening was found in the initiation of fibrillation, which was then followed by strain hardening as fibrils were drawn into the neck region. Strain rate was found to peak at the craze boundaries, consistent with the surface drawing mechanism from TEM results. During craze fibrillation, the local strain rate of the drawn polymer increased with drawing strain until a critical strain εh was reached; beyond that, the strain rate decreased with the strain. The critical strain εh, identified as the onset of strain hardening, was found to decrease with entanglement density νe in the low-νe, craze-forming regime but become a constant in the high-νe regime where crazing was replaced by shear yielding. The transition between crazing and shearing is controlled by the tendency of strain localization in the entanglement network.

Interrelationships between Reinforcing-Bar Physical Properties and Seismic Demands

A theoretical study was performed on the interrelationships between reinforcing-bar physical properties and seismic demands for Grade 60 steel in beams of reinforced concrete rigid frames subjected to a limiting lateral drift of 2%. The study indicates that the generally accepted requirement of a minimum tensile/yield ratio of 1.25 for reinforcing steel in seismic design is both prudent and probably satisfactory. However, considering high steel strains exhibited in the calculations, particularly for beams having a small ratio of length to depth, the study strongly suggests that it would be prudent, for seismic-resistant reinforced concrete structures, to either specify A706 steel or to specify A615 steel to have at least a 10% minimum elongation in 8 in (203 mm). For reinforcing in very squatty beams (with close to the minimum length-to-depth ratio permitted by ACI 318-95), the calculations indicate that the stress-strain curve for the reinforcing steel should not exhibit too low a tangent modulus of elasticity at onset of strain hardening (possibly causing ductility capacity to be exceeded) or too high a tangent modulus (possibly causing tensile strength capacity to be exceeded).

鉄筋コンクリートはり柱接合部における付着すべり

Parametric analyses were carried out. Variable was the height of the column. Design criteria was proposed to prevent the bond failure of beam bars in the joint. The length of the yield penetration region in the joint was evaluated by the following equation, [numerical formula] where μ was the ductility factor, ε_y was the yield strain of beam bar, ε_<SH> was the strain at the onset of strain hardening, and l' was the shear span length of the beam. The effects of the pull-out from the joint upon the bond failure of column bars in short columns were also studied. Considering these effects, design criteria to prevent the failure was proposed.