Early Strain Localization Research Articles

Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability

In modern sheet metal forming processes, such as hydroforming and single point incremental forming, sheet metals are often subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. However, the effect of these out-of-plane stresses on the onset of plastic strain localization is not considered when classic necking criteria are used, as the latter are generally formulated based on the plane stress assumption. The main objective of the present investigation is to overcome this limitation by developing numerical tools and analytical relations that allow considering the influence of these compressive stresses on the prediction of localized necking. In the different tools developed, and for comparison purposes, finite strain versions of both the deformation theory of plasticity and the rigid-plastic flow theory are used to describe the mechanical behavior of the metal sheet. Furthermore, both the bifurcation theory and the initial imperfection approach are employed to predict the onset of strain localization. Various numerical predictions are reported to illustrate the effect of normal stress on the occurrence of localized necking in sheet metals. From these different results, it is clearly demonstrated that out-of-plane stresses may notably enhance sheet metal formability and, therefore, this property can be effectively used to avoid the initiation of early strain localization.

Martensite size effects on damage in quenching and partitioning steels

Quenching and partitioning steels create new opportunities for light-weight automotive component design, however, a deeper understanding of microstructural damage and failure mechanisms is essential to improve these materials. Here we study the strain partitioning and damage behavior of these steels by carrying out in-situ high resolution microstructure and micro-strain mapping experiments. These investigations reveal that the presence of coarse martensite laths leads to early strain localization, especially when they are in the vicinity of untempered martensite islands. Future alloy design and heat treatment design efforts should thus particularly focus on eliminating copresence of coarse martensite laths and untempered martensite.

Interaction of the Portevin–Le Chatelier phenomenon with ductile fracture of a thin aluminum CT specimen: experiments and simulations

An attempt is made here to capture numerically slant ductile fracture and its early slant strain precursors via combining a dynamic strain aging (DSA) model with ductile damage models. In recent experimental studies it has been shown that in an AA2XXX alloy strain localization in slant bands preceded the onset of damage, originating slant fracture ahead of a notch. Here tensile tests are performed at different strain rates revealing some negative strain rate sensitivity which is an indication of DSA effect for AA2198-T8. A McCormick-type DSA model in conjunction with a Rousselier damage model, a reduced polycrystalline plasticity model and a Coulomb fracture criterion for slip systems have been used. Full 3D finite element simulations using this model and typical parameters for aluminum alloys capture the early strain localization in slanted bands, their intermittent activity and the final slant fracture. Prior simulation results without the DSA model and others using the von Mises plasticity or the GTN model did not capture the early slant strain localization thereby suggesting that DSA may well be the physical origin of the early slant strain localization and final slant fracture phenomena in this alloy.

Behavior of RC beams strengthened with strain hardening cementitious composites (SHCC) subjected to monotonic and repeated loads

Ultra High Performance Strain Hardening Cementitious Composites (UHP-SHCC) is a newly developed construction material, has large advantages on large strain capacity as well as high compressive and tensile strength, which is useful for strengthening or repair concrete members. However, some important obstacles need to be studied, such as the strain localization occurs in the UHP-SHCC strengthening layer around the substrate concrete cracks, which severely limits the ductility of the strengthened beam subjected to monotonic and repeated loads. In the present study, ten specimens were tested experimentally, which divided into two major groups, each group contains five specimens, one as a control and four strengthened with constant UHP-SHCC layer thickness having variable reinforcement ratios embedded in the middle of the strengthening layer. Two types of loading were applied; Monotonic loading for the first group and short time repeated loading for the second group. The recorded tests showed that use additional reinforcement embedded in the strengthening layer for beams strengthened with UHP-SHCC become sufficient at certain limit to eliminate the observed early strain localization and to gain adequate ductility under both monotonic and repeated loading. Another important conclusion is the strengthening of RC structures using an unreinforced UHP-SHCC layer may lead to a brittle failure especially in case of repeated loading.

Interactions between propagating rotational rifts and linear rheological heterogeneities: Insights from three‐dimensional laboratory experiments

The lateral propagation of rifts is a consequence of the relative divergence of lithospheric plates about a pole of rotation. Modern and ancient examples of rifts are known to overprint pre-existing linear anisotropies in the crust and lithosphere, such as lithospheric boundaries, crustal sutures, and thermal anomalies. Here we investigate how propagating rifts interact with pre-existing structures by using three-dimensional analogue experiments with rotational extensional boundary conditions and variably oriented linear weak zones in the lithospheric mantle. When linear weaknesses are oriented at low angles to the rift axis, early strain localization occurs in narrow domains, which merge at later stages, resulting in continental break up by unzipping. Strong strain partitioning is observed when the linear heterogeneity is oriented at high angles with respect to the rift axis. In these experiments, early sub-parallel V-shaped basins propagate toward the pole of rotation until they are abandoned and strain is transferred entirely to structures developed in the vicinity of the strongly oblique weak lithosphere zone boundary. The experimental results are characterized in terms of their evolution, patterns of strain localization, and surface topography as a function of the lithospheric heterogeneity obliquity angle. Comparison of the experiments to ancient and modern examples in nature may help to elucidate the common but still poorly understood process of propagating rift-lithospheric heterogeneity interaction.

A Critical Assessment of Cyclic Softening and Hardening Behavior in a Near-α Titanium Alloy During Thermomechanical Fatigue

Thermomechanical fatigue behavior of Ti-alloy Timetal 834 has been studied at two temperature intervals viz. 573 K to 723 K (300 °C to 450 °C) and 723 K to 873 K (450 °C to 600 °C) under mechanical strain-controlled cycling. Among the temperatures studied, the alloy exhibited initial cyclic softening followed by cyclic hardening at 723 K (450 °C) in the temperature interval of 573 K to 723 K (300 °C to 450 °C). However, continuous cyclic hardening was observed at 723 K (450 °C) in 723 K to 873 K (450 °C to 600 °C). At 573 K (300 °C) and 873 K (600 °C), cyclic softening was observed in the cyclic stress response curves in both the temperature intervals. The dislocation substructure was observed to be planar in both the modes of TMF loading. Based on TEM microstructures and few unconventional fatigue tests, the observed cyclic hardening is attributed to dynamic strain aging. The reduced fatigue life at 723 K to 873 K (450 °C to 600 °C) under OP-TMF loading was attributed to the combined effect of cyclic hardening (leading to early strain localization and crack initiation), oxidation, and development of tensile mean stresses.

Nonlinear behavior of RC beams strengthened with strain hardening cementitious composites subjected to monotonic and cyclic loads

Ultra High Performance Strain Hardening Cementitious Composites (UHP-SHCC) are useful for strengthening or repairing concrete members. However there is a need to use refined analytical tools to simulate response of strengthened system. In this study, ABAQUS finite element program is used to numerically perform a parametric study including two major groups. Each group contains nine specimens strengthened from the tension side with variable thickness of UHP-SHCC and reinforced with variable reinforcement ratios embedded in the strengthening layer. Two types of loading were applied: monotonic loading for the first group and cyclic loading for the second group. ABAQUS CPS4R mesh element nonlinear is used to model the concrete, while truss element nonlinear is used to model longitudinal and transverse steel reinforcement. The numerical results obtained are in good agreement with the experimental work found in the literature. The results from the parametric study showed that it is sufficient to use 1.2% additional reinforcement ratio embedded in the strengthening layer for beams strengthened with UHP-SHCC to eliminate the observed early strain localization and to gain adequate ductility under both static and cyclic loadings.

Mechanical Properties of Ultrafine‐Grained Metals: New Challenges and Perspectives

Investigations of the behavior of ultrafine‐grained (UFG) materials manufactured by severe plastic deformation (SPD) have been greatly motivated by the expectations that they may have unique properties as well as by the desire to understand the fundamental mechanisms underlying the specific properties associated with extreme grain refinement. Although the concurrent improvement of both strength and ductility is possible via SPD, the most commonly observed high strength of UFG materials is paired with a very limited uniform elongation. Based on the dislocation kinetics and its relation with the Considère instability, an attempt is made to provide a unified view for the hardening behaviour and early macroscopic strain localization.

Strain-path change induced transients in flow stress, work hardening and r-values in aluminum

Commercially pure aluminum with random texture was prestrained either by rolling or by uniaxial compression, and then tested in uniaxial tension to study the transients in flow stress, work hardening and r-value induced by the strain-path change. New experimental results are reported on the variation of the r-value and the permanently reduced work hardening subsequent to the strain-path change. A continuum plasticity model was developed that can reproduce the observed behavior. The model applies a second-order “delayed pointer” tensor to represent the microstructural anisotropy and was implemented into the finite element software LS-DYNA. The model was calibrated to the experimental data, and a simulation of early strain localization subsequent to an orthogonal strain-path change was compared to strain fields measured by a digital image correlation technique.

Micro-strain Evolution and Toughening Mechanisms in a Trimodal Al-Based Metal Matrix Composite

A trimodal metal matrix composite (MMC) based on AA (Al alloy) 5083 (Al-4.4Mg-0.7Mn-0.15Cr wt pct) was synthesized by cryomilling powders followed by compaction of blended powders and ceramic particles using two successive dual mode dynamic forgings. The microstructure consisted of 66.5 vol pct ultrafine grain (UFG) region, 30 vol pct coarse grain (CG) region and 3.5 vol pct reinforcing boron carbide particles. The microstructure imparted high-tensile yield strength (581 MPa) compared to a conventional AA 5083 (242 MPa) and enhanced ductility compared to 100 pct UFG Al MMC. The deformation behavior of the heterogeneous structure and the effects of CG regions on crack propagation were investigated using in situ scanning electron microscopy micro-tensile tests. The micro-strain evolution measured using digital image correlation showed early plastic strain localization in CG regions. Micro-voids due to the strain mismatch at CG/UFG interfaces were responsible for crack initiation. CG region toughening was realized by plasticity-induced crack closure and zone shielding of disconnected micro-cracks. However, these toughening mechanisms did not effectively suppress its brittle behavior. Further optimization of the CG distribution (spacing and morphology) is required to achieve toughness levels required for structural applications.

Midcrustal discontinuities and the assembly of the Himalayan midcrust

AbstractDetailed quartz lattice preferred orientation (LPO) data define two structural discontinuities in the exhumed high‐grade metamorphic core of the Himalaya exposed in the upper Tama Kosi region of east central Nepal. The structures are marked by abrupt breaks in a general trend of up structural section increasing quartz LPO‐defined deformation temperatures. Deformation associated with the upper structural discontinuity, which occurs within sillimanite grade rocks, is postpeak metamorphism in both the hanging wall and the footwall. New geochronologic data constrain the timing of metamorphism in the hanging wall of the upper discontinuity to between 24 and 16 Ma, indistinguishable from previously published ages for the footwall. Movement across this structure represents Early Miocene strain localization and thickening in the Himalayan midcrust. Movement across the lower discontinuity, which occurs between staurolite and kyanite grade rocks, appears to be synmetamorphic with material in its footwall at approximately 10 Ma, but postpeak metamorphism for material in its hanging wall. This movement is interpreted to reflect the underplating and incorporation of material into the metamorphic core. The recognition of two thrust‐sense discontinuities in the exhumed Himalayan core in the Tama Kosi region is consistent with other similar structures recognized along the Himalaya. The widespread nature of these structures reinforces that they are important to our understanding of the evolution of the kinematics of large, hot orogens.

Local Strain Hardening and Non-Uniformity of Plastic Strain of Tinplate

During evaluation of the mechanical properties of tinplate for packaging industry by uniaxial tensile test, a non-uniform plastic strain occurs very often. This phenomenon results from the fact, that the plastic deformation is not uniformly developed throughout the measured section. There is a localization of deformation in one or more places resulting in local changes of the tinplate ́s mechanical properties. This paper deals with local strain hardening and non-uniformity of plastic strain of the tinplate temper TH415CA during uniaxial tensile test. Based on micro hardness measurements in the following locally deformed areas, local changes of mechanical properties of the tinplate were determined. The reasons of early strain localization were assumed by microstructural analysis. In the present work are considering partial aspects of the problem focusing on the properties of the local strain hardening and their consequences for stability of uniform plastic strain.

In situ 3-D observation of early strain localization during failure of thin Al alloy (2198) sheet

High-resolution in situ synchrotron X-ray laminography combined with digital volume correlation (DVC) is used to measure the damage and plastic strain fields ahead of a notch introduced within a 2198 Al–Cu–Li alloy sheet. Synchrotron laminography is a technique specifically developed for three-dimensional (3-D) imaging of laterally extended sheet specimens with micrometre resolution. DVC is carried out using the 3-D image contrast caused by iron-rich intermetallic particles present in the alloy. The alloy is recrystallized and tested in T8 artificial ageing condition involving relatively low work hardening. Inclined strain localization bands are shown to develop at ∼800μm from the notch prior to the onset of damage. Damage in this region results mainly from the nucleation of voids on micrometric intermetallic particles and occurs at a very late stage of deformation, followed by very limited void growth. The accumulation of strain in the slanted localization band is found to be a steady process, whereas the crack propagation is a sudden process. Standard 3-D FE calculations using either von Mises plasticity or Gurson’s model do not capture the plastic localization process.

Strength and ductility of RC beams strengthened with steel-reinforced strain hardening cementitious composites

Abstract Strengthening of Reinforced Concrete (RC) beams using strain hardening cementitious composites (SHCCs) layer cast to their soffit has recently been investigated. That work confirmed that strain localization occurs in the SHCC-strengthening layer, which severely limits the ductility of the strengthened beam. This paper reports the ductility enhancement achieved in tests on reinforced concrete beams that were strengthened with lightly steel-reinforced SHCC layer (0.3% and 0.6% steel reinforcement ratio). It has been found that the combination of the SHCC and a small amount of steel reinforcement helps develop higher strain in the SHCC strengthening layer at ultimate load and eliminates the observed early strain localization. The recorded averaged strain at ultimate load of SHCC-strengthening layer provided with 0.3% and 0.6% steel reinforcement was 2.10 and 3.76 times that of an unreinforced SHCC layer. Also, use of a 0.6% reinforcement ratio changed the mode of failure of the SHCC-strengthened beams from brittle to more ductile. Moreover, the SHCC-strengthening layer with 0.6% reinforcement ratio was able to develop uniformly distributed visible cracks, which were the only indication that failure was imminent. It needs to be emphasized that strengthening of RC structures using an unreinforced SHCC layer may lead to a brittle failure.

An Alpine-style Ordovician collision complex in the Sierra de Pie de Palo, Argentina: Record of subduction of Cuyania beneath the Famatina arc

The Caucete Group and structurally overlying Pie de Palo Complex in western Argentina are characterised by two generations of west-verging folds and thrust-related shear zones, which formed under amphibolite facies conditions. The Caucete Group is separated from the Pie de Palo Complex by the Pirquitas thrust. These structures are interpreted to have formed as a result of a progressive deformation, generated during Middle Ordovician, underthrusting of the Laurentian-derived Cuyania microcontinent beneath the active Famatina margin. Geometrical relationships are most simply explained if the Pie de Palo Complex was basement to the Caucete Group prior to Ordovician orogenesis. We propose that this basement-cover relationship was established during Cambrian rifting of the Cuyania microcontinent from Laurentia. The Pirquitas fault may have been initiated during this extension prior to its long-lived remobilization as a thrust. We cannot rule out the possibility that the Pie de Palo Complex was exotic with respect to the Caucete Group, but for this to be possible we have to introduce an extra generation of structures, for which no evidence is preserved. The deformation was characterised by early strain localization followed by a more homogeneously distributed non-coaxial flow during F 2. Thermal softening probably dominated over fabric softening during this stage.

From granitoid to kyanite-bearing micaschist during fluid-assisted shearing (Ile d’Yeu, France)

We describe amphibolite-facies shear zones affecting an orthogneiss from the Armorican Hercynian belt (Ile d'Yeu, western France). The deformation pattern is consistent with top-to-the-South thrusting followed by E–W extension, as documented elsewhere in the region. Shearing was accompanied by channelled fluid flow that transformed the orthogneiss into a peraluminous micaschist. Structural and mineralogical data indicate rather early strain localization. Then, temperature increase associated with crustal thickening favoured more distributed deformations marked by shear zone stretching and the development of a HT regional foliation. Chemical analyses made across five shear zones show mass transfers that mainly implied losses in Ca and Na, and gains in H2O, Mg, and K. Most results indicate constant volume transformation, but some suggest records of either gains or losses of volume (between +20% and 30%). This might reflect variable records of fluid-rock interactions according to the timing of initiation and subsequent evolution of individual shear zones, early thrusting stages being marked by up-temperature flow, and late thrusting stages by down-temperature flow. d18O analyses suggest that fluids experienced significant isotopic exchange with orthogneisses.

Reconstruction of continental margin architecture deformed by the contraction of the Lagonegro Basin, southern Apennines, Italy

Thrust propagation through previously rifted continental margins may result in fold and thrust belts whose structure is strongly controlled by the inherited basin architecture, as it occurs in southern Italy. The Lagonegro units of the southern Apennines comprise a deformed pelagic basin succession showing variable stratigraphic characteristics, mainly lateral variations in both facies and thickness, interpreted to be due to a complex basin topography related to a Triassic rifting event. In contrast to previous studies, cross-section balancing and restoration indicate that the Lagonegro units exposed in the high Agri Valley area suffered relatively limited internal shortening (8 km, i.e. 35%). Early deformation of these rocks, later incorporated into a large-displacement thrust sheet, was dominated by folding around (present-day) roughly north–south-trending axes. The attainment of a regional décollement level was favoured by an early mild inversion of the basin, producing a roughly similar structural elevation of both hanging-wall and footwall successions to Mesozoic faults. Most of the contractional deformation was accommodated by buckling of the Mesozoic syn-rift strata between synsedimentary faults, which represented major mechanical interfaces. Early strain localization in the Lagonegro Basin ahead of the active thrust front was most probably mechanically controlled by a faulted crustal segment which originally lay, within the continental margin, between two massive carbonate platforms.