为什么玻璃等脆性材料的实测断裂强度比理论原子键强度低了两个数量级?Griffith 能量判据如何用微裂纹解释这一矛盾?
Why does the measured fracture strength of brittle solids like glass fall two orders of magnitude below the theoretical atomic-bond strength, and how does the Griffith energy criterion resolve this contradiction with microcracks?
若拉断全部原子键,理想强度应约为 E/10,而实际玻璃仅及百分之一量级。Griffith 指出体内预存的亚微观裂纹会把尖端处的应力放大到足以逐个剪断键的程度,并给出临界应力 σ_c = [2Eγ/(πa)]^(1/2),即裂纹越长越危险。这一能量平衡思想开创了线弹性断裂力学,后来发展为应力强度因子 K 判据。
Snapping every atomic bond would give an ideal strength near E/10, yet real glass fails at about one percent of that. Griffith argued that pre-existing submicroscopic cracks amplify the applied stress at their tips until bonds break one after another, yielding the critical stress sigma_c = [2E*gamma/(pi*a)]^(1/2), so longer cracks mean earlier failure. This energy balance founded linear elastic fracture mechanics and later evolved into the stress intensity factor K criterion.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
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出处备注：此条未指向带版次的可引用著作（通识性内容、机构文件或未展开的英文书名），本库不提供独立书目出处；如需精确引用，需由编辑补全具体篇目与版次。
Griffith A. A., Phil. Trans. R. Soc. Lond. A 221, 163–198 (1921);Irwin G. R., J. Appl. Mech. 24, 361–364 (1957)
Griffith A. A., Phil. Trans. R. Soc. Lond. A 221, 163 (1921); Irwin G. R., J. Appl. Mech. 24, 361 (1957)
#弹性与断裂 #Griffith 微裂纹判据
玻璃这类脆性材料的实测断裂强度为什么远低于理论上的原子键强度？
Why is the measured fracture strength of brittle materials such as glass far below the theoretical atomic-bond strength?
格里菲斯指出实际材料内部遍布微裂纹，应力会在裂纹尖端集中到平均应力的数百倍。裂纹失稳扩展遵循能量判据：弹性能释放率必须足以支付新生的表面能，由此得到强度与裂纹尺寸平方根成反比的格里菲斯公式。这一结果解释了脆断强度的尺寸效应，并奠定了线弹性断裂力学的基础。
Griffith recognized that real bodies teem with microcracks, where stress concentrates to hundreds of times the nominal applied stress. Unstable crack growth follows an energy criterion: the released elastic strain energy must cover the newly created surface energy, which yields Griffith's law that strength scales inversely with the square root of crack length. The result explains the size effect in brittle strength and laid the foundation of linear elastic fracture mechanics.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-04
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A. A. Griffith,《The phenomena of rupture and flow in solids》,Philos. Trans. R. Soc. Lond. A 221, 163–198,1921 (DOI: 10.1098/rsta.1921.0006)
A. A. Griffith, 'The phenomena of rupture and flow in solids', Philos. Trans. R. Soc. Lond. A 221, 163–198, 1921, DOI: 10.1098/rsta.1921.0006
独立核验依据 · Independent verification: 核验依据 1 Crossref DOI 10.1098/rsta.1921.0006
#弹性与断裂 #格里菲斯准则
为什么拍一下篮球，它会弹起来？
Why does a basketball bounce when you drop it?
球落地时被压扁，橡胶和空气把能量储存又弹回，把球推回空中；只是每次都会损失一点能量，所以越弹越低。
On hitting the ground the ball squashes and the rubber and air store energy, then push it back up. Some energy is lost each bounce, so it rises a bit less each time.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 3 条独立证据
来源 · Source
Halliday、Resnick 与 Walker，《物理学基础》（第10版）
Halliday, Resnick & Walker, 'Fundamentals of Physics' (10th ed.)
独立核验依据 · Independent verification: 核验依据 2 angusrobertson.com.au
#弹性 #能量 #篮球