氏名　SOFIAN BIN MOHD
学位の種類　博士（工学）
学位記番号　博甲第630号
学位授与の日付　平成24年8月31日
学位論文題目　Statistical Approach to Fatigue Behavior of Magnesium Alloys　（マグネシウム合金の疲労挙動への統計的アプローチ）
論文審査委員
　主査　教授　武藤　睦治
　副査　教授　井原　郁夫
　副査　教授　宮下　幸雄
　副査　准教授　大塚　雄市
　副査　富山大学　工学部　教授　石原　外美

• 論文目次
• 論文要旨
• 論文審査の結果の要旨

［平成24（2012）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

Table of Contents　page
Abstract　p.iv
Acknowledgements　p.vi
List of publications　p.vii
Table of Contents　p.viii
List of Figures　p.xii
List of Tables　p.xv
Chapter 1:　Introduction
　1.1　Magnesium alloys　p.1
　1.2　Fatigue phenomenon in material　p.6
　1.3　Phenomena of fatigue limit　p.9
　1.4　Fatigue behavior of magnesium alloy　p.10
　1.5　Fatigue and scatter　p.12
　1.5.1　Scatter in fatigue life　p.14
　1.5.2　Scatter in fatigue limit　p.19
　1.6　Statistical analysis of fatigue properties　p.22
　1.6.1　Introduction to probability and statistics　p.22
　1.6.2　Probabilistic approach to fatigue limit testing　p.31
　1.6.2.1　Conventional S-N testing　p.34
　1.6.2.2　Quantal response tests　p.35
　1.6.2.3　Accelerated stress tests　p.39
　1.7　Motivation of the present work　p.40
　1.8　Scope and objective of the present work　p.41
　References　p.43
Chapter 2:　Scatter analysis of fatigue life in die-cast magnesium alloy
　Abstract　p.57
　2.1　Introduction　p.58
　2.2　Experimental procedure　p.60
　2.3　Results and discussion　p.62
　2.3.1　Scatter behavior of fatigue life for AM60B magnesium alloys and A365-T5 aluminum alloy　p.65
　2.3.2　Statistical analysis of the fractographic pore size data　p.69
　2.3.3　Fracture mechanics life prediction　p.72
　2.3.4　Statistical analysis of the metallographic pore size data　p.73
　2.3.5　Scatter behavior of fatigue life for the wrought magnesium alloys and steel　p.77
　2.4　Conclusion　p.79
　References　p.81
Chapter 3:　Scatter analysis of fatigue limit in magnesium alloys
　Abstract　p.83
　3.1　Introduction　p.84
　3.2　Definition of fatigue limit　p.86
　3.3　Experimental procedure　p.87
　3.4　Results and discussion　p.93
　3.4.1　Scatter behavior of fatigue limit for the magnesium alloys　p.96
　3.4.2　Scatter behavior of fatigue limit for the stress at 10^6 cycles　p.97
　3.4.3　Scatter behavior of fatigue limit for the SUS630 stainless steels at 10^7 cycles　p.100
　3.4.4　Scatter behavior of fatigue limit at different fatigue lives for the magnesium alloys and stainless steel　p.101
　3.5　Conclusion　p.102
　References　p.104
Chapter 4:　Comparison of scatter behavior between fatigue and tensile properties
　Abstract　p.106
　4.1　Introduction　p.107
　4.2　Experimental procedure　p.108
　4.3　Results and discussion　p.109
　4.3.1　Scatter behavior of tensile strength for the magnesium alloys　p.109
　4.3.2　Scatter behavior of tensile strength for SNCM439 steel　p.112
　4.3.3　Comparison of scatter behavior between fatigue limit and tensile strength for the magnesium alloys and the steel　p.113
　4.3.4　Comparison of scatter behavior between fatigue limit and fatigue life for the magnesium alloys and steel　p.114
　4.4　Conclusion　p.116
　References　p.117
Chapter 5:　Conclusions
　5.1　General conclusions　p.119
　5.2　Recommendations for further work　p.121

　The struggle to decrease the weight of automotive and aerospace components becomes an important factor for the progressive growth of the use of magnesium alloys during the last few decades. In addition, consideration of statistical behavior of fatigue properties in design optimization may also facilitate in structural weight reduction. In the present study, the statistical behavior of fatigue properties for magnesium alloys has been investigated. Several types of magnesium alloys produced by different manufacturing processes have been considered. In order to understand the factor influences the scatter behavior of fatigue properties, the study has been extended to other materials i.e. aluminum alloy and steel.

Chapter 1: Introduction - A brief introduction about magnesium alloy, its fatigue behavior, scatter behavior of fatigue properties and the concept of statistical analysis have been outlined. The results of the previous studies have been reviewed to identify the important unsolved problems. The motivations encouraging the present study have been also presented.

Chapter 2: Scatter analysis of fatigue life for die-cast magnesium alloy - A series of fatigue tests were successfully conducted to obtain twenty fatigue lives data at a stress amplitude corresponding to an average fatigue life of 105 cycles. Statistical analysis carried out by using a Weibull distribution showed that the scatter in fatigue life of a die-cast AM60B magnesium alloy was almost comparable to that of a die-cast A365-T5 aluminum alloy. Pore size distributions on fracture surface as well as metallographic surface were evaluated to compare the scatter of fatigue life in both die-cast materials. Similarity of their scatter behavior suggested that pore size distribution could be used for estimating the scatter behavior of fatigue life. As expected, the scatter in fatigue life for die-cast materials were significantly large compared to those for rolled AM60B and extruded AZ61 magnesium alloys without pores. However, although fatigue crack of all SNCM439 steel specimens were nucleated from specimen surface, the resulted fatigue life scatter was very large and nearly comparable to those of die-cast materials. The complicated microstructure of SNCM439 steel would be a reason for a large scatter in fatigue life.

Chapter 3: Scatter analysis of fatigue limit for the magnesium alloys - Fatigue limit scatter data was obtained by means of testing procedure adopted in the standard test methods. The results of statistical analysis showed that the scatter of fatigue limit for the extruded magnesium alloy was slightly lower than those for the steels, while the die-cast magnesium alloy with casting pores exhibited significantly large fatigue limit scatter than those of extruded AZ61 and steels. It was also found that the fatigue limit scatter was almost consistent with those evaluated at different finite lives of 105, 106 and 107 cycles for all the materials. This suggests that the fatigue limit scatter behavior in very high cycle regime may be estimated by using the fatigue limit scatter information in high cycle regime.

Chapter 4: Comparison of scatter behavior between fatigue and tensile properties - The scatter behavior of tensile properties was evaluated by using twenty specimens. The scatter in tensile strength for the die-cast magnesium alloy was the largest among all the evaluated materials, as also observed in its fatigue limit and fatigue life scatter behavior. The scatters of fatigue limit evaluated by Weibull modulus or COV value were comparable to those of tensile strength for all the materials. This suggests that fatigue limit scatter behavior may be estimated by using the tensile strength scatter information. It was also found that the scatter in fatigue life was extremely large compared to those in fatigue limit for all the materials. This large scatter may result from the fact that fatigue life is dominantly determined by two phenomena of crack nucleation and small fatigue crack growth, while fatigue limit is determined by one phenomenon of crack nucleation.

Chapter 5: Conclusions - The general conclusions and recommendations for future work have been summarized and discussed.

　本論文は、「Statistical Approach to Fatigue Behavior of Magnesium Alloys （マグネシウム合金の疲労挙動への統計的アプローチ）」と題し、5章より構成されている。
　第1章「Introduction」では、本研究に関わる研究動向を概説するとともに、本研究の目的と範囲を述べている。
　第2章「Scatter Analysis of Fatigue Life for Die-cast Magnesium Alloy」では、ダイキャスト・マグネシウム合金AM60Bの疲労寿命のばらつきを調べ、破面で観察したき裂発生源となった鋳造欠陥寸法から破壊力学的に推定した疲労寿命が実験結果とよく一致すること、断面の組織観察から求めた鋳造欠陥寸法のばらつき特性が、疲労寿命のばらつき特性とほぼ一致することなどから、ばらつきの主要因が鋳造欠陥寸法のばらつきにあること、疲労寿命ばらつきはダイキャスト・アルミ合金のそれと同等であり、構造部材としてマグネシウム合金をアルミニウム合金に代替しても強度信頼性の観点からは特に問題はないことなどを明らかにしている。
　第3章「Scatter Analysis of Fatigue Limit for the Magnesium Alloys」では、ASTMあるいはJIS等で定められた標準疲労試験法に基づくS-N曲線から求めた疲労限度のばらつきを調べ、マグネシウム合金圧延材および引抜材では疲労限度のばらつきは十分小さく、標準試験法で求めた疲労限度は十分信頼性があること、ダイキャスト材ではばらつきが大きく、標準試験法で求めた疲労限度にはばらつきの影響があることを考慮する必要があること、疲労限度以外の105及び106で求めた疲労強度のばらつきも疲労限度の場合と同様に小さいこと、比較材として用いた機械構造用低合金鋼SNCM439は焼入れ・焼戻しによる不均一な微視組織のために単相のマグネシウム合金圧延材・引抜材に比べ大きな疲労限度のばらつきを示すことなどを明らかにしている。
　第4章「Comparison of Scatter Behavior Between Fatigue and Tensile Properties」では、引張試験より求めた引張強度のばらつきを調べ、疲労限度のばらつきと比較し、マグネシウム合金圧延材および引抜材では疲労限度のばらつきは引張強度のばらつきと同等のワイブル係数m値および正規分布のばらつき係数COV値を示し、疲労限度のばらつきは引張強度のばらつき程度と考えてよいこと、ダイキャスト材の疲労限度及び引張強度のばらつきは圧延材や引抜材より大きいが、この場合も疲労限度と引張強度のばらつきは同程度となること、このような疲労限度と引張強度のばらつきの関係は、アルミニウム合金や鋼の場合にも同様に認められることなどを明らかにしている。
　第5章「Conclusions」では、以上の研究の結果を総括的にまとめるとともに、将来の展望について述べている。
よって、本論文は工学上及び工業上貢献するところが大きく、博士（工学）の学位論文として十分な価値を有するものと認める。