Strain-induced Hardening Research Articles

Strengthening of cruciform sample arms for large strains during biaxial stretching

Material-forming abilities are crucial for the optimisation of sheet metal-forming processes. Among the many methods used for the evaluation of forming limits, those based on cruciform samples are very promising, mostly because of their frictionless character and access to a pure two-dimensional stress area. In contrary to punch or tubular test samples, they allow in-situ strain measurements on both sides of the gauge region. Nevertheless, they have some disadvantages. Namely, the arms of the sample crack at the gauge region before reaching the deformation limit. This reduces the mechanical insights that can be gained from a single specimen. The paper describes the development of cruciform specimens in which large strains can be achieved during bi-axial tensile testing. The experiments focus on the application of initial deformation on the cruciform sample arms prior to the test. Strain-induced hardening of the sample arms is shown to increase the maximum achievable strain within the gauge section. This allows the stress strain response of a given material to be characterised following large plastic deformation. The samples used in the bi-axial tensile tests each had one particular pre-deformed shape in the corners, whose degree of pre-deformation differed between them. The results demonstrate the increased strain characterisation capabilities, which can be determined from the addition of initial plastic deformation. Increased cold working was found to increase the maximum plastic deformation, and the associated data collection, which could be achieved within the test area. Selecting the correct degree of pre-deformation in the support region made it possible to increase the strain in the gauge section of the sample from ∼1% to about ∼11% without the need to build up the arms or reduce the thickness of the test area.

Thermoplastic polyurethanes with varying hard-segment components. Mechanical performance and a filler-crosslink conversion of hard domains as monitored by SAXS

When monitoring tensile tests of thermoplastic polyurethanes (TPU) by small-angle X-ray scattering (SAXS) we find a filler-to-crosslink conversion of hard domain function. Its strength is related to the chemical composition and governs the mechanical performance of the TPUs. Acting as fillers, the domains provide a high modulus of elasticity. Once the domains take load, they lose their filler function and the material gains in extensibility. All the five machine-cast TPUs have soft segments from PTHF® 1000 and a hard segment content ≈45%. The hard segments are built from different diisocyanates (DI) and diols (chain extenders, CE). The base material has hard segments made from 1,4-butanediol (BD) and methylene diphenyl diisocyanate (MDI). Two other TPUs contain as DIs either the hydrogenated, isomeric MDI (H12MDI) or hexamethylene diisocyanate (HDI), respectively. In two other materials the CE is varied. Here the BD is replaced by either the shorter 1,3-propanediol (PD) or by the longer 1,6-hexanediol (HD). A morphological model is fitted to the SAXS data. It returns nanoscopic parameters, e.g. discriminating between the total (Vt) and the crosslinked (Vx) volume of hard domains. Fillers are Vf=Vt-Vx. Results show that Vf-domains can be converted into Vx-domains. Hydrogenation of the aromatic base DI does not change Vt, but Vx lags behind. Young’s modulus is higher (filler function, high Vf), but the material breaks earlier (low Vx). Generally, Vt increases for small strains (strain-induced domains, SIDs) and decreases for strain >1. SIDs start as fillers. When MDI is replaced by HDI the formation of SIDs is boosted leading to strain-induced hardening – only at low strain. At higher strain the modulus lowers (conversion Vf→Vx). Only in this material are so many domains converted that Vx increases during stretching. The material breaks late. The long CE increases the average distance between crosslink domains and narrows the distribution of the distances. With the medium CE domains appear less stable at low strain.

Strain-Induced Crystallization of Segmented Copolymers: Deviation from the Classic Deformation Mechanism

The classic deformation mechanism of the Gaussian model of Haward and Thackray was utilized to treat the true stress−strain behaviors of a family of novel polyether-b-amide segmented copolymers based on the crystalline hard segments of polyamide1012 and the amorphous soft segments of poly(tetramethylene oxide). The results showed that the deformation behaviors of the plastic copolymers abided by the Gaussian model, causing the modulus G of the strain-induced hardening process to depend on the weight percentage of the polyamide segments in the copolymers. By contrast, the deformation of elastomeric copolymers deviated from the model because of the occurrence of strain-induced crystallization in the soft polyether sections at large strains, which negated the Gaussian assumption; i.e., the random coil conformation was maintained even under substantial stretching. The onset point of deviation was, for the first time, quantitatively identified by in situ FTIR and further confirmed by in situ WAXD/SAXS.

Evidence for a transition in deformation mechanism in nanocrystalline pure titanium processed by high-pressure torsion

Nanocrystalline titanium with an average grain size of about 60–70 nm was prepared by high-pressure torsion. The results of hardness and structural evolutions indicate that a strain-induced hardening–softening–hardening–softening behaviour occurs. For coarse-grained titanium, 〈a〉-type dislocation multiplication, twinning and a high pressure-induced α-to-ω phase transformation play major roles to accommodate deformation, leading to a significant strain hardening. As deformation proceeds, dynamic recrystallisation leads to a decrease in dislocation density, especially for 〈a〉-type dislocations, leading to a slight strain softening. The 〈c〉-component dislocation multiplication dominates the deformation when the grain size decreases to 100 nm and 〈c〉-component dislocation multiplication, grain refinement and the α-to-ω phase transformation contribute to the second strain hardening. The following strain softening is attributed to dynamic recovery.

Dispersed polypropylene fibrils improve the foaming ability of a polyethylene matrix

We compare the foaming ability of metallocene catalysed polyethylene (mPE) with that of mPE containing fibrillated polypropylene (PP) domains (mPE/fibrillated-PP) and mPE containing spherical PP domains (mPE/spherical-PP). We observe that mPE/fibrillated-PP shows the best foam morphology with the highest number of bubbles per unit volume. We explain this enhancement in foaming ability through rheological and crystallization studies. We identify that the fibrils form a percolated network at a fibril content of 4.5 wt% using the Winter-Chambon analysis. The network of entangled fibrils results in strain hardening in uniaxial extension. Shear thickening responses are observed in shear flow. Such responses are not observed for mPE or mPE/spherical-PP. Oscillatory shear flow investigation of the isothermal melt crystallization reveals a two decade decrease in the time for the onset of crystallization in the mPE/fibrillated-PP and a decade decrease in mPE/spherical-PP relative to neat mPE. We attribute the enhancement in foaming ability of mPE/fibrillated-PP to the concurrent increase in strain-induced hardening response and improved crystallization kinetics.

Effect of hardening temperature on the phase composition and wear resistance of roll steels with 5% Cr

The effect of a wide range of hardening temperatures on the capacity of cold-rolling roll steels with 5% Cr (65Kh5SMF and 9Kh5SMF) for strain-induced martensitic transformation and hardening is determined. The abrasive wear resistance of the steels is studied.

Absence of rippling in graphene under biaxial tensile strain

Recent experiments [C. H. Lui, L. Liu, K. F. Mak, G. W. Flynn, and T. F. Heinz, Nature (London) 462, 339 (2009)] on graphene grown on ultraflat substrates have found no rippling in graphene when subject to temperature cycling. Unsupported/unstrained films of graphene as well as films grown on various substrates on the other hand have been found to show rippling effects. As graphene grown on a substrate is invariably strained, we examine the behavior of the out-of-plane acoustic-phonon mode with biaxial tensile strain. This mode is generally associated with the rippling of graphene. We find that it can be fit to a relation of the form ${w}^{2}=A{k}^{4}+B{k}^{2}$, where $w$ and $k$ are the frequency and wave vector, respectively. The coefficient $A$ is found to show a weak dependence on strain while $B$ is found to increase linearly with strain. The strain-induced hardening explains the absence of rippling in graphene subject to biaxial strain. In addition, we find that graphene when subject to a biaxial tensile strain is found to undergo a structural transition with the mode at K going soft at a strain percentage of 15%.

The Filamentous Actin Cross-Linking/Bundling Activity of Mammalian Formins

Formins are multidomain proteins that regulate actin filament dynamics and are defined by the formin homology 2 domain. Biochemical assays suggest that mammalian formins display actin-filament nucleation, severing, and bundling activities. Whether formins can cross-link actin filaments into viscoelastic arrays and the effectiveness of formins' bundling activity compared with that of important filamentous actin (F-actin) cross-linking/bundling proteins are unknown. Here, we used rigorous in vitro rheologic assays to deconvolve the dynamic cross-linking activity from the bundling activity of formin FRL1 and the closely related mDia1 and mDia2. In addition, we compared these formins with the canonical F-actin bundling protein fascin and cross-linking/bundling proteins alpha-actinin and filamin. We found that FRL1 and mDia2, but not mDia1, can help F-actin form highly elastic networks. FRL1 and mDia2 mediate the formation of highly elastic F-actin networks as effectively and rapidly as alpha-actinin and filamin but only past a relatively high actin-to-formin molar ratio of 50:1. Past that threshold molar ratio, the mechanical properties of F-actin/formin networks are independent of formin concentration, similar to fascin. Moreover, unlike those for alpha-actinin and filamin but similar to those for fascin, F-actin/formin networks show no strain-induced hardening. mDia1 cannot bundle F-actin but can weakly cross-link filaments at high concentrations. Point mutagenesis reveals that reducing the barbed-end binding activity of FRL1 and mDia2 greatly enhances the rate of formation of F-actin gels but does not significantly affect the mechanical properties of the resulting networks at steady state. Together, these results suggest that the mechanical behaviors of FRL1 and mDia2 are fundamentally different from those of cross-linking/bundling proteins alpha-actinin and filamin but qualitatively similar to the mechanical behavior of the bundling protein fascin, albeit with a dramatically increased (>10-fold) threshold concentration for transition to bundling, which nevertheless leads to much stiffer F-actin networks than fascin.

Hardness and shear band evolution in bulk metallic glasses after plastic deformation and annealing

Strain-induced hardening and annealing-induced softening are typical in crystalline metals. Bulk metallic glasses (BMG) exhibit the opposite behavior, namely, strain-induced softening and annealing-induced hardening. In addition, reversible softening–hardening–softening occurs in a BMG subjected to a three-step deformation–annealing–deformation process. The hardness changes after deformation and annealing can be correlated with the shear band patterns around/underneath Vickers indents. Shear bands produced during indentation of as-cast BMG are semicircular and radial, consistent with the stress distribution beneath the indenter. In contrast, the shear bands in the pre-strained BMG are irregular and convoluted, and appear to be a mixture of the shear bands produced during the prior compression and those in the as-cast BMG. After annealing, the shear bands tend to recover their semicircular and radial shapes consistent with the annealing-induced hardening.

Elongation flow-induced morphological change of a diblock copolymer melt of polystyrene and poly(ethylene propylene)

The elongational flow-induced alignment process of a lamellar-forming polystyrene-b-poly(ethylene propylene) (SEP) diblock copolymer has been investigated by using elongational flow opto-rheometry (EFOR) and small angle X-ray scattering (SAXS). The lamellar domains of the compression molded SEP were aligned in a preferred direction by roll casting at 200°C. In the EFOR measurement, the roll-cast film was uniaxially elongated at 180°C at a Hencky strain rate, ε˙o, of 0.01s−1 in the direction either perpendicular (denotes case I) or parallel (case II) to the direction of the lamellar normal. The apparent retardation, Rapp, and initial moduli data measured during elongation suggest that either polystyrene (PS) or poly(ethylene propylene) (PEP) domain is preferentially elongated during the early stage of elongation. Transient elongational viscosity, η(ε˙o;t), measured during the case I elongation exhibits a continuous increase up to rupture with the absence of a morphological change. One measured during the case II elongation shows an initial increase up to 20s, followed by a slight decrease by 80s prior to a predominant increase before rupture. The SAXS patterns of the elongated samples show that the lamellar domains subjected in the case I elongation persist during elongation without any prominent structural change, whereas those subjected in the case II elongation are highly deformed and rotated by about 90°, displaying a strong strain-induced hardening in the final stage of elongation.

Functional Synergy of Actin Filament Cross-linking Proteins

The organization of filamentous actin (F-actin) in resilient networks is coordinated by various F-actin cross-linking proteins. The relative tolerance of cells to null mutations of genes that code for a single actin cross-linking protein suggests that the functions of those proteins are highly redundant. This apparent functional redundancy may, however, reflect the limited resolution of available assays in assessing the mechanical role of F-actin cross-linking/bundling proteins. Using reconstituted F-actin networks and rheological methods, we demonstrate how alpha-actinin and fascin, two F-actin cross-linking/bundling proteins that co-localize along stress fibers and in lamellipodia, could synergistically enhance the resilience of F-actin networks in vitro. These two proteins can generate microfilament arrays that "yield" at a strain amplitude that is much larger than each one of the proteins separately. F-actin/alpha-actinin/fascin networks display strain-induced hardening, whereby the network "stiffens" under shear deformations, a phenomenon that is non-existent in F-actin/fascin networks and much weaker in F-actin/alpha-actinin networks. Strain-hardening is further enhanced at high rates of deformation and high concentrations of actin cross-linking proteins. A simplified model suggests that the optimum results of the competition between the increased stiffness of bundles and their decreased density of cross-links. Our studies support a re-evaluation of the notion of functional redundancy among cytoskeletal regulatory proteins.

Flow birefringence and strain-induced hardening of cycloolefin copolymers under elongational flow

Strain-induced hardening behavior and flow birefringence were studied on copolymers of ethylene–tetracyclododecene (E–TD) and ethylene–norbornene (E–NB) of various compositions subjected to uniaxial elongation with constant Hencky strain rate between 0.01 and 1.0 s −1 in the temperature range from +40 to +60°C above their respective glass transition T g. When compared at the corresponding temperature of, e.g. T g+50°C, the E–TD copolymer exhibited stronger tendency of strain-induced hardening than the E–NB copolymer of the corresponding comonomer content. The stress optical rule (SOR) was obeyed for the E–NB copolymer in the whole range of its composition, while for the E–TD copolymer, the SOR was valid only for that of low TD content (<30 mol%), but invalid for that of high TD (≥30 mol%) content. The results suggest that the increase in the population of bulkier TD comonomer may be a molecular origin of the strong strain-induced hardening as well as a reason for the invalidity of SOR for the E–TD copolymer of high TD content. For the two copolymers that satisfy SOR, the stress optical coefficient C decreases exponentially with the comonomer content, and the tendency is stronger for E–TD than for E–NB, reflecting the comonomer size. The stress optical coefficient C vs. composition plots of the E–NB (block type) and E–TD copolymers are extrapolated at zero E limit to 5.5×10 −10 and 7.5×10 −12 Pa −1, respectively, which are expected to be the C for the NB and TD homopolymers if such polymers do exist.

A House of Cards Structure in Polypropylene/Clay Nanocomposites under Elongational Flow

This Letter describes the first real space observation for the formation of a house of cards structure in polypropylene/clay nanocomposite melt under elongational flow by TEM analysis. Both strong strain-induced hardening and rheopexy features are originated from the perpendicular alignment of the silicate layers to the stretching direction.

Elongational flow birefringence of ethylene–tetracyclododecene copolymer

Simultaneous measurements of transient tensile stress σ( ϵ ̇ 0;t) and birefringence Δn( ϵ ̇ 0;t) were conducted under uniaxial elongation with constant Hencky strain rate ϵ ̇ 0 on new olefin-copolymer of ethylene (E) and tetracyclododecene (TD) of three different TD content from 20 to 41 mol%. For the low TD content copolymer, the extentional viscosity η E ( ϵ ̇ 0;t)(≡σ( ϵ ̇ 0;t)/ ϵ ̇ 0) showed only moderate increase with elongation time t or Hencky strain ϵ(= ϵ ̇ 0t) and the stress optical coefficient C( ϵ ̇ 0;t)(≡ Δn( ϵ ̇ 0;t)/σ( ϵ ̇ 0;t)) was nearly constant for the whole range of σ examined. On the other hand, for other samples of high TD content (≥30%), we observed strong uprising of η E often referred to as strain-induced hardening, and rapid decrease in C with increasing σ. As the copolymer chains were stretched out from the entangled state, the larger amount of the bulky TD groups in the latter may suppress the flow-induced conformational change to take place and suppress the disentangling of the chains, leading to the increase in σ and decreasing of C.

Elongational flow-induced morphology change of block copolymers Part 1. A polystyrene-block-poly(ethylene butylene)-block-polystyrene-block-poly(ethylene butylene) tetrablock copolymer with polystyrene spherical microdomains

Simultaneous measurements of transient tensile stress and birefringence are conducted as a function of Hencky strain rate ϵ̇0 and elongation time t on a polystyrene-block-poly(ethylene butylene)-block-polystyrene-block-poly(ethylene butylene) tetrablock copolymer with a weight fraction of polystyrene (PS) of 0.205, which displays spherical morphology. The measurements are carried out at high temperatures between the glass transition temperature of PS and the order–disorder transition temperature (TODT∼190°C) of the block copolymer under uniaxial elongation with ϵ̇0 between 0.01 and 1.0s−1. The data exhibit strain-induced softening under high ϵ̇0 (∼1.0s−1) at low temperatures, but strain-induced hardening under low ϵ̇0 (∼0.01s−1) at high temperatures. The stress-optical coefficient C(ϵ̇0;t) is almost constant under high ϵ̇0 at low temperatures, close to the value of low-density polyethylene melt (∼2.2×10−9Pa−1), whereas it increases by approximately 10–50 times under low ϵ̇0 at high temperature. The plots of the C(ϵ̇0;t) vs. t/aT (aT being the WLF shift factor) are roughly fitted into a single curve, indicating that the C(ϵ̇0;t) depends on t/aT, rather than Hencky strain ϵ. Such behavior, especially under low ϵ̇0, reflects the contribution of form birefringence Δnf of the deformed PS domains. Small angle X-ray scattering and transmission electron microscopy observation reveal that under high ϵ̇0, the spherical PS-domains are not appreciably changed, whereas under low ϵ̇0, they are deformed into cylinders and oriented along the direction of elongation, thereby resulting in the large contribution of Δnf.

Elongational Flow-Induced Higher-Order Structure Development in a Supercooled Liquid of a Metallocene-Catalyzed Syndiotactic Polystyrene

The development of higher-order crystalline structure induced by uniaxial elongation with constant Hencky strain rates ε0 was investigated in the temperature range of 110−140 °C on supercooled liquid of a metallocene-catalyzed syndiotactic polystyrene (s-PS) via elongational flow opto-rheometry (EFOR), temperature-modulated differential scanning calorimetry, Rayleigh scattering, and polarized Fourier transform infrared spectroscopy. In the elongation at 110 °C where spherulite growth was neglected, chain-segment orientation along the flow preceded and flow-induced crystallization took place rather suddenly at a Hencky strain of ε(t) (≡ ε0t) ≈ 1.2 with the crystalline lamellae irregularly growing transverse to the oriented chains. On the other hand, at 130 °C where spherulite growth was rapid, strain-induced hardening due to the spherulite growth was observed in the early stage, and transformation of the spherulites into rodlike morphology followed, accompanying the increasing of birefringence. At 140 °C elongation with a low strain rate of ε0 = 0.01 s-1, stable spherulites were formed in the early stage, and the subsequent growth of the spherulites dominated the elongation behavior. However, at 140 °C elongation with high ε0 (≥0.1 s-1), formed spherulites were appreciably deformed along the flow direction. Thus, the features of the flow-induced structure development were governed by the dimensionless strain rate that was the ratio of ε0 to the spherulite growth rate under the quiescent state. For some semicrystalline polymers, the critical value of the dimensionless strain rate, below/above which the spherulite growth/oriented crystalline formation dominate, increases in order of the decreasing spherulite growth rate, i.e., s-PS, poly(ethylene terephthalate), and poly(ethylene naphthalate).

The equatorial small-angle scattering during the straining of poly(ether ester) and its analysis

A method for the quantitative analysis of two-dimensional (2D) small-angle X-ray scattering (SAXS) patterns with fiber symmetry by successive information filtering is proposed and applied to a series of images recorded during a straining experiment of a two-phase polymer sample at a synchrotron beamline. The studied equatorial scattering is similar to the frequently discussed void scattering, but originates from an ensemble of rodlike soft domains (needles) in the sample, orientated in the direction of strain. The intensity is extracted and projected onto the equatorial plane, the ideal two-phase structure is extracted, and the 2D chord distribution is computed. This curve describes a 2D two-phase morphology made from needle cross-sections embedded in matrix material. Because interparticular correlation is found to be weak in the chord distribution, pure particle scattering is assumed. Modeling the needle cross-sections by circular disks leads to a simple theory, which allows the deconvolution of a disk diameter distribution from the chord distribution. It is shown how parameters of the disk diameter distribution can be computed without deconvolution. For the selected poly(ether ester) thermoplastic elastomer the study of the soft domain needles indicates strain-induced hardening. While for low elongation ϵ the soft needles are more compressible than the microfibrillar matrix, saturation is observed for ϵ > 2.5. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 975–981, 1999

Elongational flow and birefringence of low density polyethylene and its blends with ultrahigh molecular weight polyethylenet

Via elongational flow opto-rheometry (EFOR), simultaneous measurements of tensile stress σ(t) and birefringence Δn(t) were conducted on a low density polyethylene (LDPE) melt and its blends with an ultra-high molecular weight polyethylene (UHMWPE) at 140°C under transient elongational flow with constant tensile strain rate ʵ0. The transient elongational viscosity nE(t)σ0 of LDPE melt first gradually increases with time t following the linear viscoelasticity rule in that ηE(t) is 3 times the shear viscosity development. 3η(t), at low shear rate γ up to a certain critical strain, beyond which ηE(t) tended to increase rapidly with t. The behaviour was often referred to as strain-induced hardening. For LDPE melt both σ(t) and Δn(t) versus tensile strain ɛ(t) (=ɛ0 t)curves were dependent on ɛ0 in such a manner that the stress optical coefficient C(t) ≡ Δ(t)/σ(t)) was independent either of ɛ0, ɛ(t), ɛ(t) or σ(t). Addition of UHMWPE up to 10 wt% to LDPE melt increased the levels of both σ(t) and Δn(t), but the tendency of strain-induced hardening was reduced. The C(t) was again independent either of ɛ0, ɛ(t) or σ(t) and also essentially independent of molecular weight (MW) and its distribution (MWD) or the blend ratio. For both LDPE and the blends the C(t) value roughly agreed with that (= 2.2 × 10−9 Pa−1) reported for shear flow experiments, thus confirming the val dity of the so far established stress optical rule.

Tensile Ductility of Superplastic Al2O3-Y2O3-Si3N4/SiC Composites

Si3N4/SiC composites are ceramic materials that exhibit excellent performance for high-temperature applications. Prepared from an ultrafine amorphous Si-C-N powder, sintered materials are constituted mainly of a β-Si3N4 matrix with SiC inclusions and have a very small grain size (less than 1 μm). Such a microstructure is propitious for superplastic forming. Superplasticity has been studied in tension, from 1550° to 1650°C, under nitrogen atmosphere. Elongations over 100% have been achieved. In many cases, at the highest temperatures and slowest strain rates, materials are damaged by different processes, including microcracking, cavitation, and chemical decomposition. A map of the most suitable (strain-rate/temperature) domain has been established. It allows the prevention of any structural alteration by selecting carefully the testing conditions. Since specimens suffered considerable strain-induced hardening, sources for this phenomenon are examined. Although the experiments have involved high temperature and extensive strain, neither static nor dynamic grain growth has occurred. Crystallization of the amorphous grain-boundary phase, which is reported in most cases, may be invoked. However, based on microstructural observations, it is not the unique origin for flow hardening.