Paul C. Paris

Stress Analysis of Cracks

and may b e t r a n s m i t t e d t o t h e E x e c u t i v e S e c r e t a r y , The p a p e r i s s u b j e c t t o m o d i f i c a t i o n and i s n o t t o b e p u b l i s h e d as a whole o r i n p a r t p e n d i n g i t s release by t h e S o c i e t y t h r o u g h t h e E x e c u t i v e S e c r e t a r y , T h i s advance copy T a b l e of C o n t e n t s. Ab s t r a c t I n t r o d u c t i o n Thermal Stresses S t r e s s-I n t e n s i t y-F a c t o r s f o r t h e Bending of P l a t e s and S h e l l s Couple S t r e s s Problems w i t h Cracks E s t i m a t i o n of S t r e s s I n t e n s i t y F a c t o r s f o r some Cases of P r a c t i c a l I n t e r e s t-i

Sub-critical flaw growth☆

Abstract The major evidence bearing upon sub-critical flaw growth in structural materials is reviewed and discussed. Attention is focused upon the growth of pre-existing flaws at operating stresses less than the net section yield strength, from both the separate and combined effects of fatigue and aggressive environments. In Section 1, the applicability of fracture mechanics concepts to flaw growth is considered, and it is demonstrated that the stress intensity factor may be viewed as the driving force for both fatigue crack growth and environmental cracking under static load. This allows a correlation of test results from different specimen geometries, and also a correlation between test results and service failures. Environmental cracking under static load is considered in Section 2. Steels and titanium alloys in various environments of water, water vapor, hydrogen, and oxygen are discussed. For steels, crack growth in water and saturated water vapor is a thermally activated process. The crack growth activation energy agrees well with the measured value for diffusion of hydrogen. The role of oxygen in inhibiting sub-critical flaw growth in vapor environments is discussed. Fatigue crack growth is considered in Section 3. It is shown that the stress intensity range is the major factor governing crack growth rates and fatigue life, with frequency and mean load as secondary variables. Crack growth rate laws are considered, and it is demonstrated that the fourth power law holds over the widest range. For an astonishing variety of steels, the fatigue crack growth rate is insensitive to composition, microstructure, and strength level, when the growth rate is plotted as a function of the stress intensity range. The combined effects of fatigue and aggressive environments are considered in Section 4. Some of the environmental behavior patterns in static loading are observed to carry over to fatigue loading. A lack of data for stress intensity ranges less than the threshold is noted. In Section 5, engineering applications are emphasized. Relationships among flaw size, threshold stress intensities in different environments, and proof and operating stresses are presented graphically and their interpretation is discussed. For 4340 steel, the role of yield strength level is summarized in a diagram which indicates that environmental cracking is the major problem at yield strengths in excess of 180 ksi, while fatigue crack growth is the major problem at lower strength levels.