含隨機缺陷電廠結構與設備元件之數值模擬與力學分析

Abstract

針對電廠結構與設備元件而言，隨機缺陷難免出現。然而，此類結構力學性能之完整性評估是相當棘手的問題。回顧2012年我國某一核電廠反應器壓力槽支撐裙板螺栓之斷裂事件，雖螺栓已經更換，坊間仍然存在修復後再次發生類似事件的疑慮。人們也擔心，假使同樣或類似事件再度發生，該支撐裙板是否仍然具備足夠的安全承載能力。如何以定量化且科學、不偏向的方式說服大眾，即是本研究之主要考量與目的。緣此，本研究提出一種合理可行的有限元素數值分析模型，處理需要考量大量隨機數據、雖簡化、但有效率且準確之力學分析，並結合統計檢定等相關學理處理分析結果。該結果既符合力學分析原理，也將不確定性所引致之風險納入考量，而達到前述本研究之目的。事實上，前述核電廠反應器壓力槽支撐裙板螺栓斷裂之力學分析也出現在美國電力研究院所出版的組件檢測導則中。該導則主要針對電廠反應器爐內組件無法檢測到的區域進行力學分析與檢測建議，但該分析保守假設裂紋具對稱性且穿壁，致使結構強度降低，並未探討裂紋隨機出現的問題。為改善該項保守假設，本研究採用前述所提模型與方法，另為較為合理的分析，並適當驗證分析結果。 綜觀電廠的安全評估問題，不單只是系統結構組件上的力學問題，對於安全至關重要的電氣電子設備也同樣存在類似的問題：隨機缺陷。美國核管會曾發佈對相關設備進行環境驗證的導則，但大多數以電氣設備較為完整，雖也曾針對含半導體電子構裝元件設備的物理失效機制進行一系列的研究，認為其若架設在溫和環境，也須證明其可正常運作而不致影響電廠設備安全運轉，但電子設備不斷推陳出新，規範導則則卻無法符合潮流，監測或儀控設備的核心元件在物理失效問題上僅能仰賴半導體設計廠商的數據，反觀目前大部分對此類電子構裝元件的可靠度研究中，則都是以完整、不含缺陷的構裝體為出發點考量，對於疲勞壽命的評估，往往忽略製程上所導致的缺陷問題。本研究延續前半部份一些理念，引用合理簡化模型的概念，配合經由數值實驗、力學公式所推導的模擬含空孔無鉛錫球之等效圓柱體及通式，將不同類型空孔在錫球內部以及隨機含空孔錫球在全域電子構裝元件分佈位置模擬出來，藉以評估其在加速環境下之疲勞壽命分佈，且引用適當的加速因子模型，推估其在電廠環境下的壽命，提供此類主動元件在維護上的參考。

As random defects presenting in a system or electronic components, it is indeed quite difficult to solve such structural integrity and mechanical problems. Reviewing the anchor-bolt failure event of reactor pressure vessel support skirt in a domestic nuclear power plant in 2012, at that time there were doubts about the reoccurrence of similar incidents thereafter although the loosen bolts have been replaced. If the failure event of anchor bolts reoccurred, the question whether there is still enough tightening capacity to ensure safety of the whole system remains. Aiming to convince the public in an appropriate and quantitative manner that is not extremely conservative, this research begins with a proposed finite element model that handles a large number of random events and improves the efficiency of the analysis. Statistical tests and other related assessments to deal with such a random problem are also proposed. In fact, such a problem also appears in guidelines issued by the Electric Power Research Institute (EPRI), which is aimed at analyzing the undetectable area of the reactor pressure vessel shourd support (the two inner and outer circular weldments aside the support plate). However, the overall assessment is merely based on the assumption of symmetric through-wall cracks to reduce the structural strength for conservative reasons. The possible issue on random events is not explored. In this study, an improved analysis in consideration of random fracture anchor bolts is proposed to improve the treatment of cracked support plate. The efficiency method is verified with a large number of random events. It also shows in this dissertation that the proposed analysis for the discrete structures can also be applied to the continuous structures. In the viewpoint of safety assessment on power plants, the random defects problem not only belongs to the mechanical issue of systems, structures and components, but also occurs on safety related electrical and electronic equipment. In fact, the US Nuclear Regulatory Commission (USNRC) has issued guidelines for environmental qualification for electrical and electronic equipment, but with little mentioning about the microprocessor-based equipment, despite a few studies on the physical failure of semiconductor-based equipment have been carried out in non-nuclear industry. Those guidelines considered that even under mild environments, such equipment should function normally without affecting the safe operation of power plants. However, the new type of microprocessor-based equipment, especially those used for monitoring and instrumentation continues to develop but its failure only relies on the testing or analyzing data from semiconductor manufacturers. Most reliability studies of the electronic packaging are based on assuming integrated structures, and the evaluation of fatigue life often ignores defects induced in production process. To improve the shortcomings, the concept of rational model proposed in the first part of this dissertation is adopted, and an equivalent general formula for use in the simulation of lead-free solder ball containing void is derived in the second part of the dissertation. The formula results in simplified equivalent cylinders to replace sloder balls containing random voids for use in the finite element simulation of packages. The fatigue life distribution of a package used in electrical or electronic equipment is determined under an accelerated environment. Its life under the normal operation of power plant can also be obtained. The result is also helpful for the maintenance of a power plant.