Peculiarities of the rheological behavior and structure formation of aluminum under deformation at near-solidus temperatures

This paper deals with a peculiar rheological behavior of aluminum at near-solidus temperatures. It has been experimentally established that there is an inverse strain rate dependence of strain resistance at temperatures ranging between 560 and 640°С and strain rates ranging from 0.06 to 1.2 s-1. Electron backscatter diffraction analysis has shown that at temperatures ranging between 540 and 640°С and strain rates ranging from 0.06 to 0.1 s-1, the main process of softening is dynamic polygonization, resulting in in situ recrystallization. At higher strain rates, ranging between 0.8 and 1.2 s-1, and temperatures ranging between 560 and 640°С, the recovery is dynamic. This unusual behavior of the mechanism of softening and the presence of the inverse strain rate dependence of strain resistance can be explained by blocking the motion of free dislocations by foreign atoms, which occurs at strain rates ranging between 0.06 and 0.1 s-1. This process results in dislocation pile-up, thereby causing in situ recrystallization. At strain rates exceeding 0.16 s-1, there is no intensive blocking of dislocations, leading to a direct strain rate dependence of strain resistance.     

Synthesis of glass ceramics from kaolin and dolomite mixture

Cordierite-and anorthite-based binary glass ceramics of the CaO-MgO-Al₂O₃-SiO₂ (CMAS) system were synthesized by mixing local and abundant raw minerals (kaolin and doloma by mass ratio of 82/18). A kinetics study reveals that the activation energy of crystallization (Ea) calculated by the methods of Kissinger and Marotta are 438 kJ·mol-1 and 459 kJ·mol-1, respectively. The Avrami parameter (n) is estimated to be approximately equal to 1, corresponding to the surface crystallization mechanism. X-ray diffraction (XRD) analysis shows that the anorthite and cordierite crystals are precipitated from the parent glass as major phases. Anorthite crystals first form at 850℃, whereas the μ-cordierite phase appears after heat treatment at 950℃. Thereafter, the cordierite allotropically transforms to α-cordierite at 1000℃. Complete densification is achieved at 950℃; however, the density slightly decreases at higher temperatures, reaching a stable value of 2.63 kg·m-3 between 1000℃ and 1100℃. The highest Vickers hardness of 6 GPa is also obtained at 950℃. However, a substantial decrease in hardness is recorded at 1000℃; at higher sintering temperatures, it slightly increases with increasing temperature as the α-cordierite crystallizes.     

Microstructural evolution of a superaustenitic stainless steel during a two-step deformation process

Single- and two-step hot compression experiments were carried out on 16Cr25Ni6Mo superaustenitic stainless steel in the temperature range from 950 to 1150℃ and at a strain rate of 0.1 s-1. In the two-step tests, the first pass was interrupted at a strain of 0.2; after an interpass time of 5, 20, 40, 60, or 80 s, the test was resumed. The progress of dynamic recrystallization at the interruption strain was less than 10%. The static softening in the interpass period increased with increasing deformation temperature and increasing interpass time. The static recrystallization was found to be responsible for fast static softening in the temperature range from 950 to 1050℃. However, the gentle static softening at 1100 and 1150℃ was attributed to the combination of static and metadynamic recrystallizations. The correlation between calculated fractional softening and microstructural observations showed that approximately 30% of interpass softening could be attributed to the static recovery. The microstructural observations illustrated the formation of fine recrystallized grains at the grain boundaries at longer interpass time. The Avrami kinetics equation was used to establish a relationship between the fractional softening and the interpass period. The activation energy for static softening was determined as 276 kJ/mol.     

Hot deformation behavior of uniform fine-grained GH4720Li alloy based on its processing map

The hot deformation behavior of uniform fine-grained GH4720Li alloy was studied in the temperature range from 1040 to 1130℃ and the strain-rate range from 0.005 to 0.5 s?1 using hot compression testing. Processing maps were constructed on the basis of compression data and a dynamic materials model. Considerable flow softening associated with superplasticity was observed at strain rates of 0.01 s?1 or lower. According to the processing map and observations of the microstructure, the uniform fine-grained microstructure remains intact at 1100℃ or lower because of easily activated dynamic recrystallization (DRX), whereas obvious grain growth is observed at 1130℃. Metallurgical instabilities in the form of non-uniform microstructures under higher and lower Zener–Hollomon parameters are induced by local plastic flow and primary γ′ local faster dissolution, respectively. The optimum processing conditions at all of the investigated strains are proposed as 1090–1130℃ with 0.08–0.5 s?1 and 0.005–0.008 s?1 and 1040–1085℃ with 0.005–0.06 s?1.     

Global Existence and Optimal Decay Rate of the Compressible Magnetohydrodynamic Equation with Potential Force

In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations(MHD) with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L~p-L~q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L~q-norm with 2≤q≤6 and its first derivative in L~2-norm when the initial perturbation is bounded in L~p-norm with 1≤p6/5.     

The periodic solution for a kind odd order delay differential equation

In this paper, we use the coincidence degree theory to research the odd order delay differential equation a(t)χ(2n+1)(t)+b(t)χ(t)+g(t,-τ(t)))=p(t), and we obtain the sufficient conditions for the existence of periodic solutions, which improves and generalizes some related results in the literatures.     

The Reverse Hoelder Classes in Martingale Setting

In martingale setting, it has been shown that Ap weights can be factorized in terms of A1 weights. This factorization benefits many problems very much. ]n this paper, the new class of RH~ plays the same role for RHs, which makes the reverse HOlder inequalities hold with exponent s＞1, that the class A1 does for Ap class. Therefore, the Jones‘ factorization theorem for Ap weights was extended to include some information about the reverse HOlder classes. And it is the most convenient obiect in weight theory indeed.     

Gracefulness of several unconnected graphs with wheel

In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥1,t ≥1, let n =2t +3, 2t +4, which proved W_n∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful; for p ≥1, t ≥1,let n=2t+3,2t+4, then W_(n,2n+1)∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful and for m≥1,r ≥1, let n =2m +5, W_(n,2n+1) ∪( C_3∨K m) U St( r)is graceful.     

A new second-order Mehrotra-type predictor-corrector algorithm for SDO

In Zhang's recent works,a second-order Mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had O(n~(3/2)log(X~0)~T·S~0/ε) iteration complexity based on the NT direction as Newton search direction. In this paper, we extend the second-order Mehrotra-type predictor-corrector algorithm for linear optimization to semidefinite optimization and discuss the polynomial convergence of the algorithm by modifying the corrector direction and new iterates. It is proved that the iteration complexity is reduced to O(n~(3/2)log(X~0)~T·S~0/ε), which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization.     

Vertex disjoint cycles in intersection graphs of bases of matroids

The intersection graph of bases of a matroid M=(E, B) is a graph G=G~I(M) with vertex set V(G) and edge set E(G) such that V(G)=B(M) and E(G)={BB′:|B∩B′|≠0, B, B′∈B(M), where the same notation is used for the vertices of G and the bases of M. Suppose that|V(G~I(M))| =n and k_1+k_2+…+k_p=n, where k_i is an integer, i=1, 2,…, p. In this paper, we prove that there is a partition of V(G~I(M)) into p parts V_1 , V_2,…, V_p such that |V_i| =k_i and the subgraph H_i induced by V_i contains a k_i-cycle when k_i ≥3, H_i is isomorphic to K_2 when k_i =2 and H_i is a single point when k_i =1.     

Research on a Class of Equations over Finite Fields

Let F_q stand for the finite field of odd characteristic p with q elements(q=p~n,n∈N)and F_q~* denote the set of all the nonzero elements of F_q.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over F_q:f(x _1,x _2,...,x _n)=(a_1 x_1 x_2~d+a_2 x_2 x_3~d...+a_(n-1)x_(n-1)x_n~d+a_n x_n x_1~d)~λ-bx_1~(d1)x_2~d2...x_n~(dn),with a_i,b∈F_q~*,n≥2,λ0 being positive integers,and d,d_i being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h_1~λ=h_2 with λ being positive integer and h_1,h_2∈F_q[x _1,x _2,...,x _n].It extends the results of the Markoff-Hurwitz-type equations.     

Novel blast furnace operation process involving charging with low-titanium vanadium–titanium magnetite carbon composite hot briquette

An innovative process of blast furnace (BF) operation involving charging with low-titanium vanadium–titanium magnetite carbon composite hot briquette (LVTM-CCB) was proposed for utilizing LVTM and conserving energy. In this study, the effect of LVTM-CCB charging ratio on the softening, melting, and dripping behaviors of the mixed burden was explored systemically, and the migration of valuable elements V and Cr was extensively investigated. The results show that with increasing LVTM-CCB charging ratio, the softening interval T₄₀-T₄ increases from 146.1℃ to 266.1℃, and the melting interval T_D-T_S first decreases from 137.2℃ to 129.5℃ and then increases from 129.5℃ to 133.2℃. Moreover, the cohesive zone becomes narrower and then wider, and its location shifts slightly downward. In addition, the recovery ratios of V and Cr in dripped iron first increase and then decrease, reaching maximum values of 14.552% and 28.163%, respectively, when the charging ratio is 25%. A proper LVTM-CCB charging ratio would improve the softening–melting behavior of the mixed burden; however, Ti(C,N) would be generated rapidly in slag when the charging ratio exceeds 25%, which is not favorable for BF operation. When considering the comprehensive softening–melting behavior of the mixed burden and the recovery ratios of V and Cr, the recommended LVTM-CCB charging ratio is 20%.     

Evolutions of diffusion activation energy and Zener–Hollomon parameter of ultra-high strength Al-Zn-Mg-Cu-Zr alloy during hot compression

The changes of stress level for the ultra-high strength Al-Zn-Mg-Cu-Zr alloy were described by constitutive equation with considering lattice diffusion of aluminum, zinc, magnesium and copper. Zener–Hollomon(Z)parameter expression based on the constitutive equation with considering lattice diffusion was used to reflect the changes of microstructure. The critical stress σcfor the initiation of dynamic recrystallization(DRX) was introduced to calculate the Z parameter. Steady-state dislocation density ρsatand critical dislocation density ρcfor the initiation of DRX decreased with the increase of deformation temperature. The dependence of diffusion activation energy Q on temperature and strain rate was given and the effects of deformation conditions on Q were discussed in detail. Microstructural evolution revealed that low angle boundaries(2–5°) created in the process of dynamic recovery(DRV) could convert into subgrain boundary, thus the original grains were divided into subgrains, and then subgrains transformed into DRX grains by the way of progressive rotation. When the Z value was high(ln Z 30.9), DRV was the main softening mechanism. With the decrease of Z value, both of DRV and DRX played an important roles in softening effect, while with the further decrease of Z value(ln Z 28.6), DRX became the main softening mechanism. Continuous dynamic recrystallization(CDRX) and discontinuous dynamic recrystallization(DDRX) operated together under the condition of lower Z value, but CDRX was confirmed as the dominant DRX mechanism.     

Effect of high temperature and high strain rate on the dynamic mechanical properties of Fe-30Mn-3Si-4Al TWIP steel

The dynamic mechanical properties of Fe-30Mn-3Si-4Al twinning induced plasticity (TWIP) steel were studied by the split-Hopkinson pressure bar (SHPB) at temperatures of 298–1073 K and strain rates of 700, 2500, and 5000 s?1. The TWIP steel indicates strain rate hardening effect between 700 and 2500 s?1, but it shows strain rate softening effect between 2500 and 5000 s?1. In addition, the strain rate softening effect enhances with an increase in deformation temperature. After deformation, the microstructures were studied by optical microscopy (OM). It is shown that the deformation bands become more convergence, a part of which become interwoven with an increase in strain rate, and the dynamic recovery and recrystallization are enhanced with an increase in both temperature and strain rate.     

Ranks of repeated-root constacyclic code

By the discussion of division in \(F_{^{^{^{_2 m} } } } \left[ u \right]/\left\langle {u^4 } \right\rangle \), the minimal spanning set and the rank of a (1 + u + u ²) - constacyclic code with an arbitrary length N = 2 ^e n over \(\Phi \) are determined based on the factorization of (x ⁿ - 1) over \({F_{{2^m}}}\).     

Multi-pattern matching algorithm with wildcards based on bit-parallelism

Multi-pattern matching with wildcards is a problem of finding the occurrence of all patterns in a pattern set{p~1,---,p~k}in a given text t. If the percentage of wildcards in pattern set is not high,this problem can be solved using finite automata. We introduce a multi-pattern matching algorithm with a fixed number of wildcards to overcome the high percentage of the occurrence of wildcards in patterns. In our proposed method,patterns are matched as bit patterns using a sliding window approach. The window is a bit window that slides along the given text,matching against stored bit patterns. Matching process is executed using bit wise operations. The experimental results demonstrate that the percentage of wildcard occurrence does not affect the proposed algorithm's performance and the proposed algorithm is more efficient than the algorithms based on the fast Fourier transform. The proposed algorithm is simple to implement and runs efficiently in O(n+d(n/σ)(m/w))time,where n is text length,d is symbol distribution over k patterns,m is pattern length,and σ is alphabet size.     

An algorithm for the spectral immunity of binary sequence with period 2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

To resist the fast algebraic attack and fast selective discrete Fourier transform attacks, spectral immunity of a sequence or a Boolean function was proposed. At the same time, an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented, here N is a factor of 2 ⁿ ? 1, where n is an integer. The case is more complicated when the period is even. In this paper, we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k - error linear complexity algorithm. Then, an algorithm for spectral immunity of binary sequence with period N = 2 ⁿ is obtained. Furthermore, the time complexity of this algorithm is proved to be O(n).     

A generalized funk’s section theorem for measures

If L is a star body in R~n whose central(n-i)-slices have the same(n-i)-dimensional measure μ_(n-i)(with appropriate density)as the central(n-i)-slices of an origin-symmetric star body K,then the corresponding n-dimensional measures μ_n of K and L satisfy μ_n(K)≤μ_n(L).This extends a generalized Funk’s section theorem for volumes to that for measures.     

Lüroth Expansion Digits and Maclaurin's Inequality

It is well known that for almost all real number x, the geometric mean of the first n digits d_i(x) in the Lüroth expansion of x converges to a number K_0 as n→∞. On the other hand, for almost all x, the arithmetric mean of the first n Lüroth expansion digits d_i(x) approaches infinity as n→∞. There is a sequence of refinements of the AM-GM inequality, Maclaurin's inequalities, relating the 1/k-th powers of the k-th elementary symmetric means of n numbers for 1≤k≤n. In this paper, we investigate what happens to the means of Lüroth expansion digits in the limit as one moves f(n) steps away from either extreme. We prove sufficient conditions on f(n) to ensure divergence when one moves away from the arithmetic mean and convergence when one moves f(n) steps away from geometric mean.     

Dissolution characteristics of sericite in chalcopyrite bioleaching and its effect on copper extraction

The effects of sericite particle size, rotation speed, and leaching temperature on sericite dissolution and copper extraction in a chalcopyrite bioleaching system were examined. Finer particles, appropriate temperature and rotation speed for Acidithiobacillus ferrooxidans resulted in a higher Al3+ dissolution concentration. The Al3+ dissolution concentration reached its highest concentration of 38.66 mg/L after 48-d leaching when the sericite particle size, temperature, and rotation speed were -43 μm, 30℃, and 160 r/min, respectively. Meanwhile, the sericite particle size, rotation speed, and temperature can affect copper extraction. The copper extraction rate is higher when the sericite particle size is finer. An appropriately high temperature is favorable for copper leaching. The dissolution of sericite fitted the shrinking core model, 1-(2/3)α-(1-α)2/3=k₁t, which indicates that internal diffusion is the decision step controlling the overall reaction rate in the leaching process. Scanning electron microscopy analysis showed small precipitates covered on the surface of sericite after leaching, which increased the diffusion resistance of the leaching solution and dissolved ions.