科技英语翻译 铝镁合金.docx

Analyses on the Flow Stress of an Al-Mg Alloy During Dynamic RecoveryA comprehensive analysis on flow stress of a wrought Al-Mg alloy is performed to examine the effect of strain. For this study, hot compression tests were carried at different temperatures and strain rates. Corrections of friction and adiabatic heating effects lead to the true stress-true strain curves in the form of dynamic recovery, which reach to a steady-state condition. After correction, constitutive analysis at a constant strain is carried out using hyperbolic-sine equation. The effect of strain on each constitutive parameter is studied to derive a strain-dependent constitutive equation based on hyperbolic-sine equation. Some of constitutive parameters reach to the constant values at the specific strain values. Also, the relations between Zener-Holloman parameter and steady-state values of strain and stress are achieved. In order to develop a strong and general flow stress equation, stress-strain curves are normalized to their steady-state values, which results in an almost similar normalized stress-strain behavior for all of the studied deformation conditionsKeywords ：Al-Mg, constitutive analysis, dynamic recovery, flow stress, hot deformation铝镁合金动态回复中流变应力的研究关于铝镁合金流变应力的综合分析是用来反映应变的影响。在这项研究中，压缩实验将会在不同的温度以及应变率下进行。修正摩擦因素与绝热因素的影响最后得到在动态恢复中达到稳态条件下时的真应力应变曲线。修正后用hyperbolic-sine方程在恒定应变下分析本构关系。分析本构关系中每个参数对应变的影响可以得到一个依赖于应变的本构方程。某些本构关系中的参数将会在应变达到一个特定值后也变为恒值。同样，还可以得到Z参数与稳态应变应力之间的关系。为了得到一个正确的普遍通用的流变应力方程，将会对应力应变曲线进行修正达到稳态值，进行拟合后得到的真应力应变方程将会对其他的变形条件研究提供借鉴。关键词：铝镁合金，本构分析，动态回复，流变应力，热变形。1. IntroductionThe flow stress of metals during hot deformation is one of the main interesting properties of any specific material produced by hot deformation processes such as hot rolling and forging. The Al-Mg aluminum alloys are strategically used in special industries such as aerospace and military because of their high strength-to-weight ratio as well as their other benefits (Ref 14). Rolling or any tensile-related deformation of this alloy at the elevated temperature in the case of as-cast is limited because of its low ductility and high sensitivity to hot cracking. Hence, it needs a pre-process such as hot extrusion for modifying the cast structure and increasing the hot ductility for subsequent processes (Ref5). Therefore, it is interesting to find the complete behavior of the produced wrought alloy during hot deformation前言特殊材料在热变形生产比如轧制、锻造过程的流变应力是一种非常重要并且有意义的属性。铝镁合金因其具有高强度低重量等优点而是被用在航天器和军事上的并具有战略意义的一种材料。这种铸态合金的轧制以及任何的拉伸变形都在逐渐升高的温度环境下进行，这是因为合金本身有较低的延展性并对高温敏感。因此，为了后续的变形它需要进行像挤压一样的连续变形来改善铸结构增加热韧性。因此，研究合金在生产的热变形过程中的复杂行为是非常有意义的。Three important parameters in hot deformation are temperature, strain, and strain rate (Ref6). In contrast to the analyses of the effects of temperature and strain rate on hot deformation, the effect of strain has been receiving far less attention and consideration. For aluminum alloys, analyses of hot deformation behavior have been carried out by some researchers, but the majority of the presented constitutive analyses at high temperatures are based on the strain rate and temperature at a constant strain (Ref1, 2, 79). In the case of Al-Mg alloy, there are no reports on the effect of strain in hot deformation constitutive equation. However, similar studies have been carried out to find the dependency of constitutive parameters on strain individually; the effect of strain on constitutive parameters is not yet clearly known. Some of the parameters may change due to the effect of strain, such as hot deformation activation energy, which is an important parameter in the discussion of related mechanism of behavior during hot deformation. For example, Fang and Zeng (Ref 10) observed the dependency of activation energy on strain. Also, some researchers (Ref1, 2) showed that this dependency is not appreciable. For aluminum alloys, no research has considered the effect of strain and its influence on all of the constitutive parameters simultaneously. In the case of non-aluminum alloys, Mirzadeh and Najafizadeh (Ref 11) showed the variations of some hot deformation parameters with strain for a 17-4 PH stainless steel and suggested an equation to predict the flow curve, but this equation is applicable only when the dynamic recrystallization occurs. Also, Slooff et al. (Ref12) investigated a strain-dependent constitutive analysis for three magnesium alloys where only the dependency of one constitutive parameter on strain has been considered, and no constitutive equation has been proposed.在热变形中的三个重要因子分别是温度，应变，应变速率。为了对比并分析温度和应变速率在热变形中的影响，应变将不会被关注和考虑。很多研究人员已经对铝合金的流变应力进行了研究。但是大部分的研究人员在高温下的研究都是在基于应变速率和温度在一个固定值。就镁铝合金而言目前还没有关于在高温下的应变方程，但是已经进行了类似的研究来发现依赖于应变的本构方程，应变在本构方程中的作用目前还不十分清楚。一些的因子可能随着应变的影响而发生变化，就像热变行激活能，它在研究热变性时的变形机理过程中关系中起着很重要的作用。比如，Fang和Zeng两个人观察了在拉力作用下的应变激活能的依赖关系。同时，一些研究人员发现这个依赖关系是不能确定的。对于铝合金，还没有实验既考虑应变的作用又同时考虑它对全部结构因子的的影响。对于非铝的合金，Mirzadeh 和Najafizadeh进行了17-4 PH不锈钢在张力的作用下热变形一些参数的变化并得到一个可以预测流变曲线的方程，但是这个方程只是在动态再结晶发生的时候才有效。同时Slooff用应力相关的方程去分析三个镁合金式样，分析过程中只考虑了本构方程中关于应变的因素，最后没有得到本构方程。However, it is interesting to examine how the constitutive equation is changed with strain and how much the strain influences the constitutive parameters. In this research, two methods have been employed to find a strain-dependent constitutive equation which described the flow stress of a wrought Al-Mg alloy during hot deformation. First, on the basis of hyperbolic-sine Arrhenius-type constitutive equation, the effect of strain on the constitutive parameters is achieved. Second, a flow stress equation based on hot flow curves and normalized flow stress curves is derived, which has a general form applicable for all of studied deformation conditions.然而，确定本构方程在应变状态下的变化情况和应变对结构因子的影响量是非常有意义的，在此研究中将会使用两个方法来寻找与应变有关的本构方程，这个方程可以描述锻造镁铝合金在热变形过程中的流变应力。第一，以hyperbolic-sine Arrhenius-type本构方程为基础，将会得到应变对结构因子的影响，第二，以热流动曲线和归一化的流变应力方程为基础，可以推断出流变应力方程。这个方程将会为动态条件下的研究提供借鉴。2. Experimental ProcedureFor this study, Al-Mg aluminum alloy received from hot extrusion of cast billet has been used. Table1 shows the chemical composition of this alloy. Isothermal hot compression tests using a cylindrical specimen with 8 mm in diameter and 12 mm in height (Ref1, 2) machined in extrusion direction of extruded billet were performed at 350, 450, and 5500C and at strain rates of 0.001, 0.1, and 1 s1 by means of an Instron 8502 hot compression machine. The temperature of the tests was controlled by a K-type thermocouple inside the furnace. The reported strain rate is the mean value which was controlled by the constant cross-head speed of the dies. A thin layer of mica was placed between the interfaces of dies and specimen for minimizing the effect of friction. Soaking time of the specimens before the test was 15 minutes, and they were immediately water quenched after the test. 在试验或者研究中，使用的是连铸坯热挤压式样。表1 显示的是这种合金的化学成分。等温热压缩试验使用的是沿着连铸坯挤压方向机加工的直径的8mm长度为12mm的式样，通过Instron 8502拉力机在变形温度为350，450，550变形速率为0.001,0.1,1的条件下进行。试验温度由深入炉子的K型热电偶来控制。名义应变速率是一个平均值，它是由具有恒定速度的模具横头来控制。在模具与样品的接触面上回放置一薄片云母以用来减小摩擦的影响。实验前要先将试样冷却15分钟，实验后快速放入水中淬火。The output of compression test was the load-stroke converted to true stress and true strain using the following equations:压缩实验中的载荷将会利用下面的公式转化成真应力和真应变。Where is the true stress, F is the load, and A is the instantaneous cross-sectional area under the load F. Instantaneous cross-sectional area, A, can be readily calculated by considering the constancy of volume during deformation and using the initial height (h0), initial cross-sectional area (A0) of the sample, and the cross-head displacement (Dh). True strain (e) is obtained as follows:Where h is the instantaneous height of the sample which can be calculated ash0h.在这个公式中是真应力，F是载荷，A是在载荷F下的瞬时横截面积。因为变形过程中体积不变的原则，瞬时横截面A可以利用样品原始高度h0，原始横截面A0横头的位移Dh来准确计算。可以由下列公式获得在这个公式中h是样品的瞬时高度，他可以被准确计算出来3. Results and Discussion3.1 Flow Stress BehaviorThe true stress-true strain curves of Al-Mg alloy during hot deformation are shown in Fig.1. The presence of friction increases the actual flow stress, and adiabatic heating generated during deformation decreases the flow stress. Owing to these effects, the true stress-true strain curves are deviated from its actual behavior. The effect of friction is more obvious at large strains, and also at higher flow stress which is achieved at lower temperatures and higher strain rates. Flow softening due to the effect of adiabatic heating is larger at higher strain rate. At low strain rate, temperature change caused by deformation is negligible (isothermal condition) (Ref13). Adiabatic heating also increases with strain because of accumulation of generated heat, and decreases with increasing the test temperature because of reduction in the strength of metal. Thus, the effects of friction and adiabatic heating are corrected using the analytic relations, the geometry, and material constants of the samples and dies. Such methods have been adopted in previous studies(Ref1, 2, 13, 14) and for the present Al-Mg alloy, the details of these corrections have been described in the previous study of the present authors (Ref 15).3.结果与讨论3.1流变应力图1所示的是铝镁合金热变形的真应力应变曲线。实际的曲线将会因为摩擦力的存在而增加，同时变形过程中的绝热加热将会使得流变曲线下降。由于这些影响，真应力应变曲线将会与实际情况有所偏离。摩擦的影响在大的应变条件下比较明显，同时在由低温度高应变速率导致的高流变应力条件下也比较明显。由于在高应变速率条件下绝热加热的影响比较明显，会发生软化。在低的应变速率下由变形引起的温度变化是还可以忽略不计。绝对增温会随着应变产生热量的积累而增加，随着实验的温度升高而降低，这是因为金属中力的减少。因此使用分析关系，几何关系，以及材料和模具的常数来修正摩擦与绝对增温带来的影响。此方法被应用于早期的研究以及目前铝镁合金的研究中，此修正法的细节在目前研究人员的早期研究中已经描述的非常详细了。Figure2 illustrates the corrected curves of true stress-true strain for all conditions. At the early stage of strain, work hardening dominates flow softening, and a rapid increase of flow stress appears. As the strain increases, hardening and softening rates reach to equal values and the curves exhibit a steady-state behavior. All the curves after correction are in the form of typical dynamic recovery characterized by a rise to a plateau followed by a steady-state flow stress (Ref6). The occurrence of dynamic recovery has been examined in prior studies of the present authors (Ref15) and other researchers (Ref1, 2).图二显示的是在所有情况下经过修正的真应力应变曲线。在应变的早期，加工硬化作用大于流变软化并会出现一个急剧增加的流变应力。随着应变的增加硬化与软化的速率会相等，曲线会出现一个稳态阶段。所有经过修正的曲线都是典型的动态回复特点也就是曲线达到最高点后会出现稳定的流变应力阶段。动态回复的发生过程已经被目前的作者以及先前的研究人员所证实。3.2 Constitutive Analysis at a Constant StrainIn order to describe the deformation behavior of the alloy at elevated temperatures, constitutive analyses are performed on the hot compression test data. Owing to the importance of strain rate and temperature in hot deformation processes, reported constitutive equations almost relate flow stress to these two parameters. Zener-Holloman parameter relates temperature and strain rate as follows (Ref6):3.2稳定应变下的本构分析为了描述合金在不同温度下的变形行为，采用热压缩变形的实验数据进行本构分析。由于在热变形过程中的应变速率和温度的重要性，名义本构方程会把流变应力与这两者紧密结合起来，Z参数与温度和应应变速率的关系如下所示Where e is the strain rate, Q is the activation energy of hot deformation, R is the gas world constant, and T is the absolute hot working temperature. On the other hand, Z is a function of flow stress. One of the most widely used equations, which describes the functionality of Z to flow stress is hyperbolic-sine equation (Ref16):在这个公式中，e是应变速率。Q是热变形能激活能，R是气体常数，T是绝对热加工温度。另一方面Z是流变应力的函数。这是一个被广泛引用的方程，它可以描述了在Z参数对于流变应力的函数性质是双曲线正弦函数Where r is the flow stress, and A, a, and n are the material constants.Combination of Eq3and4results in Eq 5 which can be used for a wide range of temperature and strain rate values在这个公式中r是流变应力，A、a和n是材料常数结合公式3、4得到公式5，公式5能够在大范围温度和应变速率条件下使用。In order to find the parameters in Eq 5, the following expressions are used为了发现公式5中的参数，将会用到下面的表达式Parameter a is selected as the best value which makes the plots log( e) versus log(sinh(ar) linear and parallel, and its average values at different temperatures have been reported (Ref 2, 9, 16). By substituting of n, Q, and a in Eq 5, the parameter A can be readily calculated. The strain which should be considered for the calculation of constitutive equation at a constant strain is the strain at the peak of the flow curve (Ref9) or the steady-state strain (Ref 1, 15), depending on the behavior of the hot flow curve (i.e., dynamic recrystallization or dynamic recovery). For this case, the strain of 0.4 is selected which is completely in the steady-state part of the curves. The values of parameters in the Eq 5 at the steady-state strain of 0.4 are listed in Table2.选取适当的a的值来使得log( e) 和 log(sinh(ar)的图像更加线性化并平行，它在不同温度下的平均值已经被报道出来了。通过取代公式5中的n, Q, 和 a后参数A可以被精确计算出来。计算本构方程时所选取的应变应该是流变曲线的波峰或者稳定阶段的应变值，这取决于热流变的行为（动态在结晶或者动态回复过程）。就此而言，选取应变量为0.4，因为此时的曲线都完全在稳定阶段。公式5在应变0.4稳定阶段时候因数的值见下表2.3.3 Variations of Constitutive Parameters with StrainTraditional constitutive analyses of hot deformation behavior do not consider the effect of strain, and the reported constitutive equations are at a constant strain. However, it should be kept in mind that some parameters may alter as the strain changes. This is important when the interpretation of the behavior of metal during hot deformation is based on constitutive equation. It is noteworthy to mention that the dependency of these parameters on strain is not appreciablealways; however, it seems to be essential to investigate this dependency for improving the constitutive analyses and achieving better understanding in respect of deformation behavior of the alloy. As the first step, owing to the strong dependency of other parameters on a, the maximum accuracy in calculation has been performed using m-file code in MATLAB software at several strains. The change of a with strain is shown in Fig.3. This variation is considerable at the early stage of deformation and vanishes as the strain reaches higher values. The exponent n has similar behavior as a. It changes sharply at low strains and then attains a constant value (Fig. 4). The strains at which a and n attain the constant values are the same. It means that, after a specific strain, these parameters are independent of strain. Such behaviors of a and n do not occur when the alloys undergo dynamic recrystallization (Ref 11). The variation of hot deformation activation energy (Q) is more interesting to study because of its importance in the interpretation of softening phenomenon and mechanism of behavior during hot deformation. Figure5 shows how hot deformation activation energy is changed with the increasing strain.3.3随着应变而变化的本构参数热变形的传统本构分析没有考虑应变的影响，而且名义本构方程都是在稳定应变下得到的。尽管如此，应该谨记的是一些其他的参数也可能引起应变的变化，重要的是关于金属热变形行为的解释都是以本构方程为基础。值得注意的是提到的这些因子和应变的相关性经常是不可估计的，尽管如此对于相关性的研究来提高本构分析加深对于合金变形行为的理解是十分有必要的。第一步，由于其他因子与a有很强的相关性，在几个应变中使用MATLAB软件中的m-file代码来在计算中获得最大的精确度。随着应变变化的a的值见表3。在早期的变形阶段时需要考虑变化，而在应变达到最大值后就不需要考虑了。指数n跟a一样有类似的行为。他在低应变变化剧烈然后获得一个稳定值。a和n在达到稳定值后是应变都是一样的。这意味着在应变达到一定值后这些因子与应变就互相独立了。当合金进行动态再结晶时a和n的这种行为是不会发生的。热变形激活能的变化对于研究是十分有意义的，这是因为它在解释软化现象和和热变形行为机理的重要性。表5 显示了热变形过程中热变形激活能是如何随着应变的增加而变化的。It can be seen that hot deformation activation energy has a sinusoidal shape after a specific strain, but only a small change occurs in the value of this parameter (2.5 kJ/mol). This amount of change in activation energy can be negligible, and it is true to say that this parameter does not change after a specific strain. Nonetheless, its sinusoidal shape may be related to dynamic phenomenon during deformation. However, since its variation is negligible, it can be concluded that the softening mechanism does not change after a specific strain, and dynamic recovery reaches a stable condition. The parameter A also alters with strain, which is demonstrated in Fig.6. Unlike the three other parameters, it has an irregular dependency on strain. Fitting curves for the variation of each parameter with strain are presented in Table3 using a power or an exponential equation可以知道的是热变形激活能在经过特殊应变后的图像是一个正弦曲线，但是这个因子值只是发生了一点变化。激活能这个数量级别的变化是可以忽略不计的，真实的是这个因子经过特殊应变后是不在变化的。经管如此，这个正弦曲线与变形过程中的动态现象有关。由于它的变化可以忽略不计可以得到一个结论就是在经过特殊应该值后的软化机理并不会发生变化，动态回复会稳定在一个值，因子A也会随着应变而发生变化具体见图6.与其他三个因子不同的是它与应变的相关度是不规则的。不同因子随着应变变化的拟合曲线见图3，使用了乘方或者指数方程。Relatively lower R-squared values for Q and A curve fitting are due to its sinusoidal shape and irregular variation, respectively. Higher R-squared value may be achieved using polynomial equations to fit parameters, as, for example, demonstrated by Mirzadeh and Najafizadeh in their study (Ref 11), but it is not always true because of non-stable behaviors of these types of equations, particularly when the number of points on the graph is not adequately enough. Such instability of a polynomial curve fitting in comparison with power curve fitting for the same number of points for parameter n is shown in Fig. 7, although the polynomial curve has higher R-squared value. On the other hand, there is not a single, unique degree of polynomials, which is the best one for all the four parameters.拟合得到较低的Q与A的平方值是由于它的正弦曲线形状和错乱变化以及分散，利用多项式来拟合因子可能会得到较高的平方值，比如在Mirzadeh 和Najafizadeh研究中所展示的那样，但并不总是正确的这是因为这种类型的等式并不稳定，尤其当图上的点的数量不充分的时候。对于因子n相同点的多项拟合曲线和功率曲线如图7所示。尽管多项拟合曲线有较高的平方值但是没有单一的唯一的多项式系数，这是四个因子中最好的。By substituting the equations shown in Table3 in Eq 5,it is possible to compute the constitutive equation at any strain通过取代表3中的等式5，可以计算出在任何应变下的本构方程。The method proposed in this section may be relatively complex and time consuming because of using long formulation after substitution of each parameter in Eq 5. It also has a mathematical base and does not consider the behavior of metal during hot deformation such as dynamic recovery. Hence, it may be interesting to develop a strain-dependent constitutive equation for interpreting the behavior of alloy during hot deformation such as the form of flow stress curves and the characteristic point made from dynamic recovery.在这部分中提到的这个方法要替换公式5中的每个因子然后公式化，所以会显得相对复杂并浪费时间。这以数学为基础并且没有考虑金属在热变形过程中例如动态回复的行为。因此获得一个本构方程是非常有意义的，这是因为它能解释合金在热变形过程中那些例如流变应力曲线和动态回复特殊点这类问题。3.4 Formulation of Steady-State ConditionThe main characteristics of stress-strain curve at the high temperature are the peak stress and strain, and steady-state stress. For the alloy which undergoes dynamic recry