Effect of two-stage aging process on mechanical properties of QAl9-4 aluminum bronze alloy
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摘要:
采用正交实验研究双级时效工艺对QAl9-4铝青铜组织与性能的影响。发现不同工艺参数对合金性能影响强度不同,影响顺序由大到小为二级时效温度>一级时效温度>一级时效时间>二级时效时间。对正交实验结果进行方差分析得到最优双级时效工艺为(150 ℃/2 h)+(500 ℃/2.5 h),并以此工艺对合金进行处理。与单级时效处理相比,双级时效处理后的合金抗压强度、极限压缩率、硬度分别提升了14.79%、25.59%和5.28%。最后对不同时效工艺处理的合金进行显微结构表征,发现性能差异来源于双级时效处理后的合金含有更多弥散分布的强化相和更少的γ2相,因此对QAl9-4铝青铜进行双级时效处理可以获得比单级时效处理更优异的性能。
Abstract:In this paper, the effects of the aging process on the microstructure and mechanical properties of QAl9-4 aluminum bronze alloy were investigated with orthogonal test. The results show that different process parameters have different effects on alloy properties, with the order of influence degree being second-order aging temperature > first-order aging temperature > first-order aging time > second-order aging time. The variance analysis of orthogonal test results showed that the optimal two-stage aging process was (150 ℃/2 h)+(500 ℃/2.5 h), and the alloy was treated by this process. Compared with the single-stage aging treatment, the compressive strength, ultimate compression ratio, and hardness of the alloy treated by the optimized two-stage aging process are increased by 14.79%, 25.59%, and 5.28%, respectively. Finally, the microstructure characterization was performed on alloys treated under different aging processes. The results reveal that the differences in properties are attributed to the alloys after two-stage aging treatment containing more dispersed enhanced phases and fewer γ2 phases.Therefore, QAl9-4 aluminum bronze alloy can obtain better performance by two-stage aging treatment than that of single-stage aging treatment.
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Keywords:
- aluminum bronze alloy /
- compressive strength /
- two-stage aging /
- orthogonal test
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坚持绿色、循环、可持续的发展路线,社会才能长期稳定的发展,经济发展必须重视自然的保护问题[1-2].然而,人类的活动还是有很多方面影响着自然平衡.因矿山地下开采空区未进行处理造成巷道变形、地表沉降、房屋开裂等对自然环境造成破坏的例子比比皆是,国内外对此问题进行的研究也不尽其数[3-4].开采环境不同,影响模式不同,研究价值及意义也就不同.
宁都硫铁矿是当地一家非常重要的矿山企业,该矿山一直采用地下开采,开采方法为浅孔房柱采矿法,矿房长60 m,开采已形成+130 m、+160 m、+190 m 3个中段,最上中段+190 m离地表标高+240 m的高程差仅为50 m.井下开采空区对应地表为居民楼、农田及公路,矿山的开采必须以地表建筑物不破坏为前提、得到百姓的默认.矿山开采至今已形成较大采空区,且采空区仅留房柱对上部围岩进行支撑.矿山开采是否造成空区失稳是该矿山工作人员一直担忧的问题.基于此,通过理论分析及现场监测、预测研究,两者对比分析、综合评判研究矿山开采的稳定性[5-6],为矿山今后的开采提供指导意见及建议.
1 上覆岩层移动变形分析
1.1 上覆岩层组合及关键层
空区上覆岩层中对岩层移动起主要控制作用的岩层为关键层[7-8],根据其定义与变形特征,假定有n层同步协调变形,则最下部的岩层为关键层.同时,根据关键层变形特征及支承特征,可得:当(qn+1)1<(qn)1时,则此时的n层为关键层.由此可知n=1,即每一个岩层组合中最下面的那个岩层为关键层.
宁都硫铁矿上覆岩层较薄,顶板岩层由下而上为较硬的石英砂岩、黏土砂土.由此可知,较硬的石英砂岩即为关键层,对上覆岩层的破坏起主要控制作用,+190 m中段石英砂岩岩层厚度约15~20 m.
1.2 岩层破坏极限跨距理论
该矿山岩层可看作为水平矩形岩层,采用托板理论进行分析[9-10],假设共有n层岩层,取其中任一i层进行研究,岩层长为L,宽度为S,厚度为hi,hi比L及S小.宁都硫铁矿特点为薄矿层开采,根据弹性薄板的假设原理可以将岩层近似为薄板[11-12],进而可以推导出第i层的物理与几何方程,物理方程:
$$ \left. \begin{array}{l} {\sigma _x} = - {E_i}z/1 - {\mu _i}^2\left( {\partial _{wi}^2/{\partial _x}^2 + {\mu _i}\partial _{wi}^2/{\partial _y}^2} \right)\\ {\sigma _y} = - {E_i}z/1 - {\mu _i}^2\partial _{wi}^2/{\partial _y}^2 + {\mu _i}\partial _{wi}^2/\partial \\ {\tau _{xy}} = - {E_i}z\partial _{wi}^2/\left( {1 + {\mu _i}} \right){\partial _x}{\partial _y} \end{array} \right\} $$ (1) 几何方程:
$$ \left. \begin{array}{l} {\varepsilon _x} = - z\partial _{wi}^2/{\partial _x}^2\\ {\varepsilon _y} = - z\partial _{wi}^2/{\partial _y}^{2}\\ {\gamma _{xy}} = - 2z\partial _{wi}^2/{\partial _x}{\partial _y} \end{array} \right\} $$ (2) x与y方向弯矩:
$$ \left. \begin{array}{l} {M_x} = - {D_i}\left( {{\partial ^2}/\partial _x^2 + {\mu _i}\partial _w^2/\partial _y^2} \right)\\ {M_y} = - {D_i}\left( {{\partial ^2}/\partial _y^2 + {\mu _i}\partial _w^2/\partial _x^2} \right) \end{array} \right\} $$ (3) 其中:Di为弯曲刚度;Ei为弹性模量;μi为泊松比;Wi(x,y)为第i层岩层扰度.n为托板的弯矩:
$$ \begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{M_n}\left( {x, y} \right) = A{q_n}\\ A = \frac{{7(3{x^2} - {L^2}/4){{({y^2} - {S^2}/4)}^2} - 7{\mathit{\mu }_\mathit{n}}{{{\rm{(}}{\mathit{x}^{\rm{2}}}{\rm{ - }}{\mathit{L}^{\rm{2}}}{\rm{/4)}}}^{\rm{2}}}{\rm{(3}}{\mathit{y}^{\rm{2}}}{\rm{ - }}{\mathit{S}^{\rm{2}}}{\rm{/4)}}}}{{{\rm{2(}}{\mathit{L}^{\rm{4}}} + {\mathit{S}^{\rm{4}}} + {\rm{4}}{\mathit{L}^{\rm{2}}}{\mathit{S}^{\rm{2}}}{\rm{/7)}}}} \end{array} $$ 进而求得:
$$ {M_{{\rm{max}}}} = 7{q_n}({L^2}{S^4} + {\mu _n}{L^4}{S^2})/128({L_4} + {S_4} + 4{L^2}{S^2}/7) $$ 最后,求出n托板的等效跨距Ln:
$$ {L_n}\sqrt {\frac{{{\rm{ - }}{F_\mathit{n}} + \sqrt {F_n^2 + 4{G_\mathit{n}}{K_\mathit{n}}} }}{{2{G_\mathit{n}}}}} $$ (4) 其中:${F_n} = 21{q_n}{S^4} - \frac{{-256{S^2}{\mathit{h}_\mathit{n}}{\mathit{\sigma }_\mathit{n}}}}{{\rm{7}}}$;Gn=21qnμnS2-64h2nσn;Kn=64hn2S4σn
依据式(4)Ln的计算结果判定托板的稳定性,当Ln计算值小于采空区跨度时,托板受到破坏,相反,Ln计算值大于采空区跨度则稳定.依据以上岩层破坏极限跨距理论,前人总结得出了关键层的厚度与关键层极限跨度的关系,根据研究成果[13-14],矿房长度不一,其所对应值不一,当矿房长度在50 m与60 m时关系如曲线图 1所示.
综合分析,矿山矿房长度60 m,关键层为石英砂岩,厚度为15~20 m.由图 1可以看出当关键层厚度在15~20 m时的极限跨度为25~40 m,即空区跨度小于25 m才能保证稳定.宁都硫铁矿开采区域内空区的跨度主要在8~10 m区间,且区域内矿房条件及结构基本相似,由此可见开采区域空区岩层稳定.
2 地表沉降灰色系统预测分析
灰色理论中最为常用的灰色预测模型是等时距GM(1,1)模型[15-16],先假设x(0)={x(0)(t1),x(0)(t2),…,x(0)(tn)}为观测得到的原始沉降量数据序列,时间步长k=ti+1-ti,r次累加后,得到新数列:x(r)={x(r)(1),x(r)(2),…,x(r)(n)},
累加一次得到等时距预测模型微分方程:
$$ \frac{{{\rm{d}}{\mathit{x}^{\left( 1 \right)}}}}{{{\rm{d}}\mathit{t}}} + a_x^{\left( 1 \right)} = \mu \left( {a, \mu \;为常数} \right) $$ 得出时间响应函数:
$$ {\mathit{x}^{\left( 1 \right)}}\left( t \right) = \left[{{\mathit{x}^{\left( 1 \right)}}\left( 0 \right)-\frac{\mu }{a}} \right]{e^{ - a\left( {t - 1} \right)}} + \frac{\mu }{a} $$ (5) 令$Y = {\left[{{x^{\left( 0 \right)}}\left( 2 \right), {x^{\left( 0 \right)}}\left( 3 \right), \cdots, {x^{\left( 0 \right)}}\left( n \right)} \right]^{\rm{T}}}$
$$ \begin{array}{l} B = \left[\begin{array}{l} - \frac{1}{2}{\left[{x_1^{\left( 1 \right)}\left( 1 \right) + x_1^{\left( 1 \right)}\left( 2 \right)} \right]^1}\\ - \frac{1}{2}{\left[{x_1^{\left( 1 \right)}\left( 2 \right) + x_1^{\left( 1 \right)}\left( 3 \right)} \right]^1}\\ \;\;\;\;\;\;\;\; \cdots \;\;\;\;\;\;\;\;\;\;\; \cdots \\ - \frac{1}{2}{\left[{x_1^{\left( 1 \right)}\left( n \right) + x_1^{\left( 1 \right)}\left( {n-1} \right)} \right]^1} \end{array} \right] \end{array} $$ 由最小二乘法[17-18]得到:[aμ]T=[BTB]-1BTY,求出a、μ值,代入式(5)中进行灰色预测[19-20].
在后续3.2小节中具体分析了监测方法,对矿区地表进行了9次(15个月周期)的沉降监测,都取得了有效的监测数据.监测结果显示监测点MB5为最大沉降点,并归纳得到MB5沉降点7次的实测沉降数据(原始序列).同时,利用灰色预测模型进行预测(图 2),预测值与实测值进行对比,结果如表 1所列.可以看出,通过灰色系统预测得到的沉降值与实际监测沉降量基本一致,灰色预测模型预测地表沉降具有一定的可靠性.
表 1 实测与预测累积沉降值Table 1. Measured and predicted cumulative settlement value时间/(年-月) 序号 沉降差/mm 实测值/mm 预测值/mm 2013-10 1 0 -8.4 / 2014-01 2 -2.4 -10.8 -14.4 2014-03 3 -7.8 -18.6 -18.8 2014-05 4 -6.7 -25.3 -24.6 2014-07 5 -7.3 -32.6 -32.2 2014-10 6 -12.3 -44.9 -42.0 2015-01 7 -7.0 -51.9 -54.8 注:“/”指未进行预测. 3 现场监测预测研究
3.1 地表沉降监测方案
地表沉降能够反映地压的变化规律,地表沉降值可以通过长期的监测获取.依据矿山井上井下对照图及空区图,预估沉降范围,最后选取沿公路及公路两边辐射的监测线路;基准点布置于预估沉降区域范围外,根据矿区实际环境,设计了合理的监测方案,方案及工作量如表 2、图 3中描述.观测采用精密水准仪,配套水准尺.
表 2 地表沉降监测方案Table 2. Surface settlement monitoring program内容 监测点数量/个 监测点位置 周期/月 工作量/次 沉降监测 32 5个基准点(BM1~BM5),
8个一级沉降观测点(MB1~MB8),
19个二级沉降观测点(MB1-1~MB9-3)15 256 3.2 结果及分析
参考有关研究者及类似监测案例的处理分析方法[21-22],对监测周期内有效的监测数据进行处理分析,绘制沉降量—时间曲线图,同时,也得到了监测周期内各监测点的最终沉降量, 如图 4、表 3.
表 3 各监测点最终沉降量Table 3. Final settlement of monitoring points监测点 沉降量/mm 监测点 沉降量/mm 监测点 沉降量/mm MB1 0.00 MB1-2 -0.88 MB6-1 -31.05 MB2 -7.10 MB2-1 -0.65 MB6-2 -32.25 MB3 -13.55 MB2-2 -3.90 MB7-1 -40.55 MB4 -29.25 MB3-1 -19.90 MB7-2 -43.20 MB5 -51.88 MB3-2 -18.50 MB8-1 -8.05 MB6 -44.00 MB4-1 -19.89 MB8-2 -2.85 MB7 -29.75 MB4-2 -25.00 MB9-1 -18.10 MB8 -17.85 MB5-1 -30.85 MB9-2 -13.45 MB1-1 -1.80 MB5-2 -32.25 MB9-3 -15.60 由图 4与表 3显示,在监测周期内,监测点基本上都发生了下沉现象,下沉级别在毫米至厘米范围内,由表 3可以看出沉降量最小为0,最大为51.88 mm;一级沉降监测点的沉降值与预想一致,普遍较大;同时还可以看出MB4、MB4-1、MB4-2、MB5、MB5-1、MB5-2、MB6、MB6-1、MB6-2、MB7、MB7-1、MB7-2的沉降量属于大值,这些监测点刚好位于公路两侧附近,也是井下采空区的正上方,产生较大沉降量的原因必然与井下矿体的开挖有关.最大沉降处为农田,在可控范围之内,但在今后的开采中矿山必须重视.对于沉降较为严重的区域,不应进行开采,并及时采取支撑、充填等措施进行防护.
4 结论
1)采用理论分析宁都硫铁矿空区岩层的稳定性,判定得出宁都硫铁矿上覆岩层现开采阶段稳定.
2)利用灰色预测模型,结合地表监测数据预测沉降量,结果显示预测沉降量与实际监测值具有一致性,说明灰色预测模型能应用于地表沉降的预测.
3)根据矿山实际情况,进行了长期的地表沉降监测,结果显示大部分监测点都具有沉降数据,下沉级别控制在毫米至厘米级别,最小为0.00 mm,最大为51.88 mm,最大沉降处为农田,沉降值在可接受范围内,但矿山在今后必须跟踪监测,引起重视.
4)矿山开采对地表及矿山本身具有一定的影响,根据分析及监测现今暂未造成失稳.但在今后的开采中开采稳定性问题必须引起重视,有必要时采取充填等防范处理措施.
王庆龙 -
表 1 QAl9-4化学成分
Table 1 Chemical composition of QAl9-4 aluminum bronze alloy
元素 Al Fe Si Ni Mn Cu 含量 8.31 2.88 0.28 0.27 0.07 余量 表 2 正交实验方案
Table 2 Orthogonal experimental scheme
实验号 A(一级时效温度)/℃ B(一级时效时间)/h C(二级时效温度)/℃ D(二级时效时间)/h 1 150 2.0 450 2.0 2 150 2.5 500 2.5 3 150 3.0 550 3.0 4 200 2.0 500 3.0 5 200 2.5 550 2.0 6 200 3.0 450 2.5 7 250 2.0 550 2.5 8 250 2.5 450 3.0 9 250 3.0 500 2.0 表 3 正交实验结果(括号内为标准差)
Table 3 Orthogonal experimental results (standard deviation in parentheses)
实验号 热处理参数 抗压强度/MPa 极限压缩率/% 硬度/HRA 1 A1B1C1D1 1 088(2.1) 20.95(0.9) 59(0.9) 2 A1B2C2D2 1 153(3.3) 22.11(0.6) 55(1.2) 3 A1B3C3D3 1 139(15.8) 25.51(1.9) 55(1.2) 4 A2B1C2D3 1 142(24.4) 23.43(1.3) 53(0.9) 5 A2B2C3D1 1 119(11.1) 24.18(0.8) 52(1.0) 6 A2B3C1D2 1 067(1.0) 16.63(0.6) 58(1.1) 7 A3B1C3D2 1 129(23.7) 23.93(1.2) 56(0.7) 8 A3B2C1D3 1 022(1.3) 15.57(0.4) 57(1.4) 9 A3B3C2D1 1 146(7.1) 22.36(0.8) 56(0.8) -
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