Strain In Thickness Direction Research Articles

Unveiling the planar deformation mechanisms for improved formability in pre-twinned AZ31 Mg alloy sheet at warm temperature

To investigate the role of pre-twins in Mg alloy sheets during warm planar deformation, the stretch forming is conducted at 200 °C. Results suggest the formability of the pre-twinned AZ31 Mg alloy sheet is enhanced to 11.30 mm. The mechanisms for the improved formability and the deformation behaviors during the planar stretch forming are systematically investigated based on the planar stress states. The Schmid factor for deformation mechanisms are calculated, the results reveal that planar stress states extremely affect the Schmid factor for {10-12} twinning. The detwinning is activated and the prismatic slip is enhanced in the pre-twinned sheet, especially under the planar extension stress state in the outer region. Consequently, the thickness-direction strain is accommodated better. The dynamic recrystallization (DRX) type is continuous DRX (CDRX) regardless of the planar stress state. However, the CDRX degree is greater under the planar extension stress state. Some twin lattices deviate from the perfect {10-12} twinning relation due to the planar compression stress state and the CDRX. The basal texture is weakened when the planar stress state tends to change the texture components.

Quantitative evaluation of fracture toughness deterioration due to Pre-strain

Previous studies presented the fracture toughness evaluation values decrease due to pre-strain by local compression. However, it was not possible to distinguish whether the cause was fracture toughness deterioration or poor crack front shape straightness due to a bowing crack front at low strain. The authors applied pre-strain without affecting the crack front shape and conducted fracture toughness tests showing that 1% pre-strain reduces fracture toughness by 50%. Furthermore, we investigated the effect of the pre-strain direction on fracture toughness, and proposed a method for converting longitudinal pre-strain to thickness direction strain and demonstrated its effectiveness.

Potential and challenges of a solid-shell element for the macroscopic forming simulation of engineering textiles

Finite element (FE) forming simulation offers the possibility of a detailed analysis of the deformation behaviour of engineering textiles during forming processes, to predict possible manufacturing effects such as wrinkling or local changes in fibre volume content. The majority of macroscopic simulations are based on conventional two-dimensional shell elements with large aspect ratios to model the membrane and bending behaviour of thin fabrics efficiently. However, a three-dimensional element approach is necessary to account for stresses and strains in thickness direction accurately, which is required for processes with a significant influence of the fabric’s compaction behaviour, e.g. wet compression moulding. Conventional linear 3D-solid elements that would be commercially available for this purpose are rarely suitable for high aspect ratio forming simulations. They are often subjected to several locking phenomena under bending deformation, which leads to a strong dependence of the element formulation on the forming behaviour [1]. Therefore, in the present work a 3D hexahedral solid-shell element, based on the initial work of Schwarze and Reese [2,3], which has shown promising results for the forming of thin isotropic materials [1], is extended for highly anisotropic materials. The advantages of a locking-free element formulation are shown through a comparison to commercially available solid and shell elements in forming simulations of a generic geometry. Additionally, first ideas for an approach of a membrane-bending-decoupling based on a Taylor approximation of the strain are discussed, which is necessary for an accurate description of the deformation behaviour of thin fabrics.

Effect of Pre-straining and Subsequent Annealing on Microstructure and Mechanical Property of Zr–Sn–Nb–Fe Zirconium Alloy

Zirconium alloy is extensively used in nuclear industries as cladding and core structural material. However, the formability and service behavior are affected due to the anisotropy of mechanical property, which is detrimental to the specific application. In this work, effect of pre-straining and subsequent annealing (PA) on microstructure and mechanical property of Zr–Sn–Nb–Fe zirconium alloy is determined by means of scanning electron microscope equipped with electron backscatters diffraction and digital image correlation technique. It is found that the basal texture intensity and grain size of as-received sample decreases after pre-straining, the work-hardening value (n) increases from 0.126 of as-received sample to 0.152 of PA samples, while the anisotropy of mechanical property decreases gradually with the increase of pre-straining level. In addition, the strength, ductility and work-hardening value (n) of the PA samples tend to be accordant in the transverse direction, rolling direction (RD) and the 45° direction when the pre-straining level reaches 8%. The basal texture is gradually weakened and dispersed along the RD after annealing, whose orientation is favorable for the activation of pyramidal 〈c + a〉 slip to accommodate to the strain in thickness direction, which leads to the lower anisotropy (featured by the r-value). The low r-value and high work-hardening value (n) are favorable for improving formability. Hence, microstructure and texture of zirconium alloy can be modified though appropriate PA process to improve the comprehensive properties.

Reduced-Integrated 8-Node Hexahedral Solid-Shell Element for the Macroscopic Forming Simulation of Continuous Fibre-Reinforced Polymers

Finite element (FE) forming simulation offers the possibility of a detailed analysis of the deformation behaviour of continuously fibre-reinforced polymers (CFRPs) during forming, in order to predict possible manufacturing effects such as wrinkling or local changes in fibre volume content. The majority of macroscopic simulations are based on conventional two-dimensional shell elements with large aspect ratios to model the membrane and bending behaviour of thin fibrous reinforcements efficiently. However, without a three-dimensional element approach, stresses and strains in thickness direction cannot be modelled accurately. Commercially available linear 3D solid elements for this purpose are rarely suitable for forming simulations since they are subjected to several locking phenomena under bending deformation, especially with large aspect ratios. To alleviate this problem, so-called solid-shell elements based on the assumed natural strain (ANS) and enhanced assumed strain (EAS) method can be used. Therefore, a locking-free explicit reduced-integrated 8-node-hexahedron solid-shell element, based on the initial work of Schwarze and Reese (2011), is implemented in the commercially available FE solver Abaqus. Its suitability for macroscopic modelling of the forming behaviour of fibrous reinforcements is outlined in this work. The presented element combines the advantages of a locking-free out-of-plane deformation behaviour of conventional thin shell elements with the advantage of maintaining a fully three-dimensional material model and geometry description.

Change in Microstructure and Mechanical Properties through Thickness with Annealing of a Cu-3.0Ni-0.7Si Alloy Deformed by Cold Rolling

Effects of annealing temperature on the microstructure and mechanical properties through thickness of a cold-rolled Cu-3.0Ni-0.7Si alloy were investigated in detail. The copper alloy with thickness of 3 mm was rolled to 50 % reduction at ambient temperature without lubricant and subsequently annealed for 0.5h at 200~900 °. The microstructure of the copper alloy after annealing was different in thickness direction depending on an amount of the shear and compressive strain introduced by rolling; the recrystallization occurred first in surface regions shear-deformed largely. The hardness distribution of the specimens annealed at 500~700 °C was not uniform in thickness direction due to partial recrystallization. This ununiformity of hardness corresponded well with an amount of shear strain in thickness direction. The average hardness and ultimate tensile strength showed the maximum values of 250Hv and 450MPa in specimen annealed at 400 oC, respectively. It is considered that the complex mode of strain introduced by rolling effected directly on the microstructure and the mechanical properties of the annealed specimens.

Construction and solution of strain model along thickness of aluminum alloy plate under plastic deformation

A thickness strain model of aluminium alloy plate under plastic deformation, based on thin plate assumption was proposed. It is found that when ratio of stress fractions is constant during in-plane loading, ratios of strain components under various loading conditions are linearly related and these points of ratios form a η–η line. Under these simple loadings, strains in thickness direction can be easily calculated by the η–η line equation without integral and differential work. When the plate is under more complicated loading conditions, the thickness can be computed by the proposed optimization and piecewise calculation model. Validation computations indicate that the relative error of the results of the presented model is less than 0.75% compared with the proven theories and FE simulation. Therefore, the developed model can be applied to engineering calculation, e.g. pre-stretching analysis of aerospace aluminium thick plate, with acceptable accuracy.

Enhanced stretch formability of rolled Mg–3Al–1Zn alloy at room temperature by initial {10–12} twins

A remarkable improvement of the stretch formability of rolled Mg–3Al–1Zn alloy at room temperature was achieved by introducing initial {10–12} twins. The activation of detwinning and basal slip in twinned region was found to effectively accommodate a thickness-direction strain and this led to an enhancement of stretch formability. The improvement was obtained in proportion to the twin volume fraction and just the twin volume fraction of ∼24% enhanced the stretch formability by ∼65%, which can be achievable at 300°C.

Study on the Formability of Square Box Deep Drawing of Tailor Rolling Blanks

As a new lightweight structural sheet metal, tailor rolled blanks has a good prospect in the future development of the automobile industry, and its formability is the current research focus. We use ABAQUS software to analyze the impacts of blank holder force, thickness ratio, die radius, shape and size of sheet metal on the movement of the transition zone and thickness direction strain on the formability of square box of tailor rolled blanks in deep drawing. The results show that, generally, in the punch and side wall corner, where thinning is more serious is a dangerous rupture area, while the inner edge of flange part is prone to wrinkle. When the BHF is 140kN, the connection between the thin side and the transition zone where thinning is severe is also a dangerous area, and even more serious, likewise when the blank thickness ratio arrives at 1.4mm/0.8mm, or the blank size 260mm*260mm, thinning is very serious at the connection between the thin side and the transition zone which is a dangerous rupture area.

A finite element model for laminated piezoelectric shell structures

AbstractThin piezoelectric laminates are used for a wide range of technical applications. A four‐node piezoelectric shell element is presented to analyse such structures effectively. In case of bending dominated problems incompatible approximation functions of the electrical and mechanical fields cause incorrect results. In order to overcome this problem the finite element formulation is based on a mixed variational principle implying six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. This allows for an interpolation of the strains and the electric field in thickness direction independent of the bilinear interpolation functions. A piecewise quadratic approach for the shear strains in thickness direction and the corresponding electric field is proposed for arbitrarily layered shells. Regarding coupling of electrical and mechanical fields this yields to an appropriate balance of the approximation functions. Numerical examples show more precise results in contrast to standard elements with lowest order interpolation functions. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Enhanced stretch formability of Mn-free AZ31 Mg alloy rolled by cross-roll rolling

Stretch formability of a Mn-free AZ31 Mg alloy rolled by the reverse cross-roll rolling was investigated at room temperature. The specimen rolled by the reverse cross-roll rolling showed superior stretch formability to that of the reference specimen. The (0002) plane texture of the specimen by the revere cross-roll rolling exhibited a low texture intensity and a circular spread of the basal pole from the ND compared with those of the reference specimen. It is suggested that the modification of basal texture by the reverse cross-roll rolling contributes to an activation of basal slip and twinning, resulting in an enhancement of the thickness-direction strain and tensile ductility. Besides, it is suggested that the coarse grain size of a Mn-free AZ31 alloy seems to enhance a stretch formability, because twins become easily generated during loading.

Enhanced stretch formability of Mg–Al–Zn alloy sheets rolled at high temperature (723 K)

The texture and stretch formability of Mg–3.0 wt.% Al–1.0 wt.% Zn–0.5 wt.% Mn alloy sheets rolled at 663 and 723 K were investigated at room temperature. The specimen rolled at 723 K exhibited weaker basal texture intensity than the specimen rolled at 663 K, and this contributed to an enhancement of thickness-direction strain under biaxial tension stress for the former, resulting in an enhanced stretch formability. The origin of weaker basal texture intensity for the specimen rolled at 723 K is discussed.

FEM analysis for hot rolling process of AM60 alloy

The rolling of AM60 sheets for 50% reduction was analyzed with DEFORM to investigate the hot deformation process. The simulated results show that the sheet velocities at the entrance (21 mm/s) and at the exit (37 mm/s) are less and larger than roll velocity, respectively. From the entrance to the neutral point, the velocity at the sheet surface is greater than that at the middle point of sheet in thickness, while that from the neutral point to the exit shows the opposite pattern. The effective strain of the sheet increases from the entrance to the exit due to the continuous reduction in thickness. In addition, the effective strain at the sheet surface reaches to 1.0 and is larger than that of 0.8 at the middle point of sheet. The difference of effective strain in thickness direction has a much stronger effect on the recrystallized fraction than on the recrystallized grain size. The minimum temperature of 347 °C is obtained at the surface contacting directly with roll and the maximum temperature 388 °C at the middle point of sheet in thickness.

Stretch formability at elevated temperature of a cross-rolled AZ31 Mg alloy sheet with different rolling routes

Cross-roll rolling with different rolling routes (unidirectional rolling and reverse rolling) was carried out on a commercial AZ31 Mg alloy sheets. In the cross-roll rolling, the roll axis was tilted by 7.5° against the transverse direction. As a result of the Erichsen tests at 433–493 K, the stretch formability of the reverse cross-rolled specimen was higher than that of the unidirectional cross-rolled specimen. The reverse cross-rolled specimen showed lower average Lankford value and higher thickness-direction strain compared with the unidirectional cross-rolled specimen. This is likely to be responsible for the enhanced stretch formability of the reverse cross-rolled specimen. The higher thickness-direction strain was attributed to more random grain distribution which may promote prismatic 〈a〉 slip toward thickness direction.

Enhanced formability at elevated temperature of a cross-rolled magnesium alloy sheet

Relationship between texture and press formability of AZ31 Mg alloy sheets processed by cross-roll rolling was investigated. The Erichsen values of the cross-rolled specimens showed superior press formability compared with those of the specimens by normal-roll rolling. The superior press formability was related to a reduction in directional dependence of the thickness-direction strain and width-direction strain normalized by the tensile-direction strain ( ɛ t/ ɛ L and ɛ w/ ɛ L). The (0 0 0 2) plane texture for the cross-rolled specimen exhibited the low texture intensity and the narrow spread of basal planes to rolling direction. The reduction of anisotropy in the width-direction strain and the thickness-direction strain was likely attributed to activation of prismatic 〈 a〉 slip and pyramidal 〈 a + c〉 slip originated from the texture modifications.

On Material Conservation Laws for a Consistent Plate Theory

In the paper, material conservation laws associated with a consistent second-order plate theory are derived, which takes shear deformations and strains in thickness direction of the plate into account. Three path-independent integrals are established. In the presence of inhomogeneities in the material (e.g., defects or cracks), energy-release rates due to the change of the configuration of such flaws can be calculated by these integrals. The resulting material forces may serve to assess the reliability of structures with cracks.

Influence of Rolling Routes on Press Formability of a Rolled AZ31 Mg Alloy Sheet

Microstructure, tensile properties and press formability of AZ31 Mg alloy sheets processed by unidirectional rolling, reverse rolling and cross rolling were investigated. The intensity in (0002) plane texture for the reverse-rolled and the cross-rolled specimens was lower than that for the unidirectional-rolled specimen. In addition, the Erichsen values of the formers were larger than those of the latter. The superior press formability for the formers could not be explained from the viewpoint of the elongation to failure, n-value, average r-value and planar anisotropy of the r-value, but it was related to a reduction in directional dependence of the thickness-direction strain and width-direction strain normalized by the tensile-direction strain (εt⁄εL and εw⁄εL). Therefore, it is suggested that the minor texture formation due to reverse rolling and cross rolling gives rise to the reduction in anisotropy of strain, resulting in the superior press formability for the reverse-rolled and cross-rolled specimens.

Interlaminar Deformation Along the Cylindrical Surface of a Hole in Laminated Composites—Experimental Analysis by Moiré Interferometry

The deformation along cylindrical surfaces of holes in tensile-loaded specimens was measured using new moire interferometry techniques. The techniques were developed and validated using an isotropic, homogeneous aluminum specimen. Two composite tensile specimens, fabricated from IM7/5250-4 pre-preg with ply lay-ups of [ 0 ° 4 ∕ 90 ° 4 ] 3 s and [ + 30 ° 2 ∕ − 30 ° 2 ∕ 90 ° 4 ] 3 s , were then examined using the new techniques. Circumferential and thickness direction displacement fringe patterns (each 3° wide) were assembled into 90°-wide mosaics around the hole periphery for both composite specimens. Distributions of strain were calculated with high confidence on a sub-ply basis at selected angular locations. The measured strain behavior was complex. Ply-by-ply trends were revealed. Large ply-related variations in the circumferential strain were observed at certain angular locations around the periphery of the holes in both composites. Extremely large ply-by-ply variations of the shear strain were also documented in both composites. Peak values of shear strain approached 30 times the applied far-field axial strain. Residual viscoelastic shearing strains were recorded in regions of large load-induced shearing strains. Large ply-group related variations in the thickness direction strain were observed in the [+30°, were then examined using the new techniques. Circumferential and thickness direction displacement fringe patterns (each 3° wide) were assembled into 90°-wide mosaics around the hole periphery for both composite specimens. Distributions of strain were calculated with high confidence on a sub-ply basis at selected angular locations. The measured strain behavior was complex. Ply-by-ply trends were revealed. Large ply-related variations in the circumferential strain were observed at certain angular locations around the periphery of the holes in both composites. Extremely large ply-by-ply variations of the shear strain were also documented in both composites. Peak values of shear strain approached 30 times the applied far-field axial strain. Residual viscoelastic shearing strains were recorded in regions of large load-induced shearing strains. Large ply-group related variations in the thickness direction strain were observed in the [ + 30 ° 2 ∕ − 30 ° 2 ∕ 90 ° 4 ] 3 s specimen. An important large-scale trend was observed in which the thickness direction strain tended to be more tensile near the outside faces of the laminate than near the mid-ply region.

An investigation of the electrostrictive property of PZT/polyurethane particulate composites

Particulate composites of the thermoplastic polyurethane (TPU) elastomer and the lead zirconate titanate (PZT) ferroelectric particles were prepared by solution casting in dimethylformamide (DMF) and then hot pressed to form thin film. X-ray diffraction results reveal the phase segregation in pure TPU was suppressed in composites. A modified Michelson interferometer has been employed to measure the electric field induced strain in thickness direction of the samples. Electrostriction coefficients of the composite decrease with increasing PZT content at low electric field. Strain reversal was observed at high electric field for the composites of more than 8 vol% PZT, it is attributed to the polarization reversal of the PZT in the composites.

Measurements of interlaminar deformation along the cylindrical surface of a hole in laminated composite materials by Moiré interferometry

The deformation along cylindrical surfaces of holes in tensile-loaded laminated composite specimens was measured by means of new moiré interferometry techniques. Two composite tensile specimens, fabricated from IM7/5250-4 pre-preg with ply lay-ups of [0 4/90 4] 3s and [+30 2/−30 2/90 4] 3s, were examined by newly developed moiré interferometry techniques. Circumferential and thickness direction displacement fringe patterns, recorded in 3° segments around one quadrant of the hole periphery, were assembled into 90°-wide mosaics for both composite specimens. Distributions of strain were calculated with high confidence on a sub-ply basis at select angular locations. Measured strain behavior was complex and displayed ply-by-ply trends. Large ply-related variations in the circumferential strain were observed at certain angular locations around the periphery of the hole in both composites. Extremely large ply-by-ply variations of the shear strain were also documented in both composites. Residual viscoelastic shearing strains were recorded in regions of large load-induced shearing strains. Large ply-group related variations in the thickness direction strain were observed in the [+30 2/−30 2/90 4] 3s specimen. An important large-scale trend was observed in which the thickness direction strain tended to be more tensile near the outside faces of the laminate than near the mid-ply region. The measured strains were compared with a spline-based three-dimensional numerical technique, resulting in a very close match.