摘 要

對於應變分佈的解析在塑性力學以及具應力集中的問題，如破壞力學而言是極為重要的課題。以往熟知的應變量測技術只能對特定位置進行點應變的觀測，而精密的儀器如干涉儀(Raman Spectroscopy)雖能以無接觸的方式進行面的量測，卻因儀器昂貴而不能廣泛用於研究或工程中。相對的，數位光學測量可以提供低價而精度高的應變分佈,是很適於推廣的應變解析利器。數位影像處理的核心在於“找尋演算法”，所謂“找尋演算法”是利用數位影像相關係數，藉著比較變形前後網格內灰階值之總合，在變形後影像中尋找變形後網格的相對位置，經由變形前後網格的相對位置，即可計算出各網格之應變量。
本研究中以數位影像測量系統分析壓痕試驗後單晶純鋁試片的塑性變形區，首先探討以影像相關法為基礎的光學量測應變軟體之精準度，分別進行下列測試(a)沿X及Y軸剛體位移之分析，(b)剛體旋轉之分析，(c)改變空間解析度對精準度之影響及(d)物體表面記號覆蓋率等系列的實驗，以驗證此軟體的精準度，其次再以此軟體對於單晶壓痕試驗造成的變形圖案進行分析。
從實驗結果中可得知，X/Y軸剛體位移的誤差值為10- 4-10- 5；剛體轉動時，當轉動角度介於0°至32°，其誤差值為10- 4，而轉動角度介於32°至90°，誤差值為10- 3；從分析軟體網格大小，可發現網格大小的選取和數位影像相關計算所得的誤差平均值並無明顯的關聯性，然而在測量應變時，受網格大小所影響的是標準差的值，當選取網格大小增加時標準差的值便跟著減小；物體表面記號覆蓋率實驗中得到，最適宜的表面記號覆蓋率在35% — 65%之間。
在探討分析軟體的精準度後，數位影像測量系統成功地驗證球形壓頭誘導的塑性變形異向性，從Von Mises strain圖的分佈中，發現在單晶試片與多晶試片有著明顯的差異，多晶試片的應變分佈顯示大約同寬度的均質應變區在壓痕周圍，可將之視為等向性的變形；相較於多晶試片，單晶試片並沒有顯示一個圓形的應變分佈，相反地，單晶試片呈現一個不規則的應變分佈，顯示了它是一個異向性變形的結果。在單晶和多晶的應變圖中，一個正值的εx(或εy)形成在中央區域且在正值εx(或εy)附近看到的是負值的εx(或εy)，這個應變梯度可以由投影和真實應變這兩個效用來加以解釋，即從壓痕變形表面的位置投影到CCD相機X方向的平面，在壓痕試驗前後X方向的相對座標位置來決定εx的值，說明CCD平面上 εx的扭曲應變，同樣地，亦可對單晶和多晶純鋁的εy應變扭曲給予合理的解釋。

Abstract

The application of the strain distribution analysis plays an important role at fracture mechanics, especially in plasticity and stress concentration. It’s known that the technique of strain measurement can be used to observe strain change at interested positions. Raman-Spectroscopy can also be achieved non-contact to determine the strain field over the surface. However, it can not be generally used in areas of research and engineering, because of it’s high cost. In contrast to Raman-Spectroscopy, the digital optic measurement provides a cheap and precise measurement method to analysis strain distribution. The digital optic method is based on the matching algorithm. The matching algorithm by using the digital-image-correlation technique tries to find, within defined search boundaries, the best position of the corresponding window in the second image by comparing the matrices of the gray scale.
In this study a novel image processing is used to analysis the plastic deformation zone of a pure aluminum single crystal after indentation test. In order to investigate the precision of the DIC software in terms of strain, a series of experiments was systematically conducted. These experiments were the rigid body displacement in the X and Y direction, the rigid body rotation, the spatial resolution of the DIC software and the influence of the mark covering area. After that, this DIC software were used to investigate the deformation pattern after indentation test.
The experiments of the precision of the DIC software show the following results. Firstly, the strain errors of the rigid body displacement in the X and Y direction can be from the order of 10-4 to 10-5. Secondly, when the rigid body rotation angle is changed from 0° to 32°, the strain error is in the order of 10-4. When the rigid body rotation angle is between 32° to 90°, the strain error is in the order of 10-3. Thirdly, the resolution of the average strain remains constant, and it is not influenced by changing the facet size. The standard deviation associated with each facet size is however increased with the reduced facet size in both X and Y directions. Lastly, the appreciable mark covering area in terms of the black/white ratio lies between 35% to 65%.
In addition to the investigation of the software’s precision, full strain field measurement was successfully applied to demonstrate indentation-induced plastic heterogeneity around a spherical indenter. There exists a different strain distribution observed from Von Mises strain mapping around the spherical indenter. The strain distribution of the ploycrystall shows a homogenous deformation zone with a constant width around the indenter, i.e., regarded as isotropic deformation. In contrast to the polycrystalline, the single crystal does not reveal a circular form of the strain distribution. In contrast, it shows an irregular form of the strain distribution which indicates an anisotropic deformation pattern. In both cases of single crystal and polycrystal, a positive strain of εx and εy is observed in the central region and a negative strain of εx and εy is observed around this center. This strain gradient can be explained due to the effects of projection and real strains.

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