JEC COMPOSITES MAGAZINE - Issue #33 - June 2007 - 72

KNOW-HOW Durability g…/… A new formula to predict the structural life of composite pipes Equation (1) links the initial strains with the times to failure. (1) In equation (1), (εƒ, tƒ) and (ε0, t0) are pairs of failure points and K is a constant that depends on the ability of glass to resist the attack of water. Equation (1) can be expressed on log – log space as: (1A) or (1B) The above equations provide the theoretical basis for the regression lines linking the initial strain “εƒ” to the corresponding time to failure “tƒ”. The coefficients “C” and “K” are determined experimentally by regression methods. The regression lines predict the times to failure when the initial strains are known, or conversely, the initial strains when the times to failure are given. Equations (1), (1A) and (1B) are different forms of the same relation. Composite pipe manufacturers and ASTM standards preferentially use form (1B). In this study, we will make use of form (1). We have used the adjective “initial” in connection with the strains. In the context of this paper, “initial” refers to the actual strain that takes place immediately upon application of the loading. The “initial” strain slowly increases in response to the gradual failure of the fibres and of the resin-glass interface. The process goes on until a critical strain is reached that makes the laminate fail. For composite pipes used to carry liquids, failure is defined as the strain at weep. Should the pipe have an impermeable liner that would not weep, then failure could be defined as the strain at break. Fig. 1: The initial strains grow to make the pipe fail when they reach critical values. Note the fast growth as the ultimate strain is approached. Note also the merger of the weep and rupture regression lines. Figure 1 shows that the regression lines for the two failure criteria (weep or rupture) merge in the long term. The reader should understand that equation (1) refers to the “initial” strains that are induced on the composite immediately upon loading. The strains in equation (1) are not the final failure strains. The subscript “ƒ” in equation (1) denotes failure and “εƒ” is the initial strain that grows to failure at the time “tƒ”. The subscript “0” designates any pair of strain and time satisfying equation (1). The coefficients “C” and “K” are determined experimentally by accepted test methods. Once these coefficients are known, the regression line can be used to predict any pair of failure points. In this paper, we use the following definitions: ε0 = ε50 is the initial strain that makes the pipe fail in t50 = 50 years. t0 = t50 is the failure time of 50 years. εƒ is the initial strain that grows to failure at the time tƒ. tƒ is the time to failure under the initial strain εƒ. The initial strain that results in long-term (usually 50 years) failure is known as the Hydrostatic Design Basis, or HDB. In this paper, the HDB is represented by the symbol “S”. The structural life of composite pipes is defined by three HDB’s: 1 – Sc or cyclic HDB. This is the initial strain that makes the pipe fail after 50 years in a cyclic pressure test performed in accordance with ASTM D2992 procedure A. The pipes are tested filled with water, and the failure criterion is weep. On log x log space, the regression line takes the form of equation (2) where, to facilitate the comparison with the other HDB’s, the number of cycles has been converted into time. (2) JEC Composites Magazine / No33 June 2007 In equation (2), Kc is the slope of the cyclic regression line and (εc)t and (εc)0 are the initial cyclic hoop strains that make the pipe fail at times “t” and “t0” respectively. Usually, “t0” is taken as 50 years, which is the same as 438,000 hours. The initial strain that makes the pipe fail in 50 years is the 50-year cyclic HDB. Therefore, entering t0 = t50 = 50 years, and (εc)0 = (εc)50 = Sc in equation (2), we obtain: The generic coefficient “K” in equation (1) has been changed to “Kc” in equation (2) to denote failure by cyclic loading. The above equation can be written as: (2A)
JEC COMPOSITES MAGAZINE - Issue #33 - June 2007

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #33 - June 2007
