Deformation mechanisms and microstructural characteristics of AZ61 magnesium alloys processed by a continuous expansion extrusion approach

The unique continuous extrusion-based severe plastic deformation approaches were proposed recently to process high-performance magnesium(Mg)alloys,while the in-depth deformation mechanisms under such complicated thermomechanical conditions were not well understood.In the present work,the fundamental deformation behaviors of AZ61 Mg alloy from 25 to 400°C were firstly examined under uniaxial compression deformation.Then the deformation mechanisms and microstructural characteristics of AZ61 Mg alloy during continuous expansion extrusion forming(CEEF)were systematically investigated by microstructural observations,finite element and cellular automata simulations.The results showed that the continuous evolutions of temperature,larger strain level and complex stress state with strain rate range of 0∼5.98 s−1 during CEEF brought the distinctive dynamic recrystallization behaviors and texture development in AZ61 Mg alloy,which were different to that of uniaxial compression deformation.In details,a remarkable grain refinement was achieved via CEEF processing due to the simultaneous actions of continuous dynamic recrystallization(CDRX)and discontinuous dynamic recrystallization(DDRX).Gradually enhanced CDRX were observed from center to edge region,which had significant effects on the texture distribution and texture strength.The c-axis of most grains rotated under distinctive shear strain following parabolic metal flow,resulting in stable fiber texture.In addition,the evolution of the internal texture of the alloy led to an obvious increase in the Schmid factor for the activation of basalc+aslip system.©2022 Chongqing University.Publishing services provided by Elsevier B.V.on behalf of KeAi Communications Co.Ltd.

Microstructure and properties of Al-0.70Fe-0.24Cu alloy conductor prepared by horizontal continuous casting and subsequent continuous extrusion forming

A novel process for manufacturing A1-0.70Fe-0.24Cu alloy conductor was proposed, which includes horizontal continuous casting and subsequent continuous extrusion forming （Conform）. The mechanical properties, electrical conductivity and the compressed creep behaviour of the alloy were studied. The results indicate that the Conform process induces obvious grain refinement, strain-induced precipitation of AI7CuzFe phase and the transformation of crystal orientation distribution. The processed alloy has good comprehensive mechanical properties and electrical conductivity. Moreover, a better creep resistance under the conditions of 90 ~C and 76 MPa is shown compared with pure A1 and annealed copper, and the relationship between primary creep strain and time may comply with the logarithmic law. The enhanced properties are attributed to the grain refinement as well as the fine and homogeneously distributed thermally stable A1Fe and A17Cu2Fe precipitation phases.

Effects of technical parameters of continuous semisolid rolling on microstructure and mechanical properties of Mg-3Sn-1Mn alloy

A sloping semisolid rheo-rolling process of Mg-3Sn-1Mn alloy was developed, and the effects of process parameters on the microstructure and mechanical properties of Mg-3Sn-lMn alloy strip were studied. The results show that the primary grain average diameter of the strip increases with the increase of the roll speed. The primary grain average diameter decreases firstly and then increases with the increase of the vibration frequency, and the tensile strength and elongation of the strip increase firstly and then decrease with the increase of the vibration frequency. The primary grain average diameter increases with the increase of casting temperature, and the tensile strength and elongation of the strip decrease correspondingly. When the casting temperature is 670℃, the roll speed is 52 mm/s, and the vibration frequency is 60 Hz, Mg-3Sn-1Mn alloy strip with good properties is produced. The mechanical properties of the present product are higher than those of Mg-3Sn-lMn alloy casting with the addition of 0.87% Ce （mass fraction）.

Principle and theoretical analysis of continuous roll forming for three-dimensional surface parts

Continuous roll forming(CRF) is a novel forming process for three-dimensional surface parts,in which a pair of bendable forming rolls is used as sheet metal forming tool.By controlling the gap between the upper and lower forming rolls,sheet metal is non-uniformly extended in the longitudinal direction while it is bent in the transverse direction during the rolling process.As a result,longitudinal bending is gained and a doubly curved surface is formed.With the rotations of the forming rolls,the sheet metal is deformed consecutively,and a three-dimensional surface part is shaped continuously.In this paper,the mechanism of the three-dimensional surface formation in CRF is set forth.Through theoretical analysis of the CRF process,the governing equations for the bending deformation in rolling process are presented.Based on the simplification on the deformation and material model,the formulation to calculate the longitudinal bending deformation is derived,and the methods to design the compression ratio and the roll gap are given,the effects of compression ratio of rolling and the width of blank sheet on the longitudinal bending curvature are analyzed.The forming experiments on typical surface parts and measured results show that forming results with good precision can be obtained by CRF process.

Microstructure and Properties of 7075Al Alloy Fabricated by Directly Combined of Spray Forming and Continuous Extrusion Forming under Different Atomization Gas Pressures

A new process consisting of the spray forming and the continuous extrusion forming for manufacturing 7075A1 alloy was proposed. The microstructure evolution, mechanical properties and the resistance to stress corrosion cracking of the alloy were studied. The results indicate that the spray forming process induces obviously grain refinement and greatly lower segregation microstructure. Besides, the Conform process produces finer grains and conduces to more uniform distribution of the precipitates of A1Cu and MgZn2 phases. The fabricated alloy shows good comprehensive mechanical properties and superb performance of stress corrosion resistance. Moreover, a better combination of the mechanical properties and the resistance to stress corrosion cracking could then be obtained under a certain condition of atomization gas pressure of 0.19 MPa. The enhanced properties are attributed to the following factors, which include the grain refinement, the fine and homogeneous distribution of A1Cu and MgZn2 phases, the high density of the extruded products, as well as the discontinuous distribution of the grain boundaries after retrogression and reaging （RRA） heat treatment.

On the generalized Cauchy function and new Conjecture on its exterior singularities

This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.

The Convergence of 1-Periodic Branched Continued Fraction of the Special Form in Parabolic Regions

Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.

APPROXIMATION OF FIXED POINTS OF STRICTLY PSEUDO-CONTRACTIVE MAPPING WITHOUT LIPSCHITZ ASSUMPTION

Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β nTx n,\ n≥1satisfying 0<α n,β n<1 ,for all n≥1;∑ ∞ n=1 α n=∞;α n→0,β n→0 as n→∞ is proved to converge strongly to the unique fixed point of T ,where T:K→K is a uniformly continuous strictly pseudo\|contractive operator with bounded range.

Microstructure, mechanical properties and deformation characteristics of Al-Mg-Si alloys processed by a continuous expansion extrusion approach

In the present work,a double-pass continuous expansion extrusion forming(CEEF) process was proposed for an Al-Mg-Si alloy,in which the diameter of rods was gradually expanded.The microstructural evolution,mechanical properties and deformation characteristics were investigated by utilizing microstructural observations,mechanical testing and a finite element method coupled with a cellular automata model.The results showed that the strength and ductility of the double-pass CEEF processed Al-Mg-Si alloys were improved synchronously,especially in artificially aged alloys.The grain size of the processed Al-Mg-Si alloy rods was refined remarkably by continuous dynamic recrystallization(CDRX)and geometric dynamic recrystallization(GDRX),and the homogeneity of microstructure was gradually improved with increasing number of processing passes.The artificially aged alloy processed with double-pass CEEF and water quenching contained fine(sub)grains and high-density dislocations,which resulted in more needle-shaped β" precipitates and a larger precipitate aspect ratio than the as-received and air-cooled CEEF alloys owing to the different precipitation kinetics.The severe cumulate strain and microshear bands were found to accelerate CDRX and GDRX for grain refinement between adjacent positions of the parabolic metal flow due to the special temperature characteristics and la rge shear straining during the CEEF process.