Plain stress condition

Xu Z and Xu X. 19 99b. Liquid-solid coupled problem of radial flow through porous media under general plain stress conditions. Chinese J. of Geomechanics, 5(1), pp.12-16... 

Kc is the critical stress intensity factor for plain-stress conditions of variable constraint in the case of static loading. The value of Ki depends on specimen thickness, geometry, and on the crack size. 

When an applied load produces a normal stress in one of the three directions (assumed to be zero), a plain-stress condition prevails. In thin films, for example, the z dimension is small compared to the other directions the approximation that the normal stress is = 0 is a good one. In this case, the equations for plain stress may be obtained from Eqs. (1.80). These strains are ... 

Equation (9.17) defines the equivalent stress Mises theory. Under plain stress conditions (biaxial) Eq. (9.17) becomes... 

The equations above are valid for plane-stress situations, i.e. for thin sheets. For thicker sheets plain-strain conditions occur at the crack tip. In that case for a thick plate of infinite width containing a crack of length 2a the fracture stress is... 

Kic is the critical stress intensity factor for static loading and plain-strain conditions of maximum constraint represents a minimum value for thick plates. 

During our test, external stresses were applied in the vertical and horizontal directions which correspond to a quasi-plain stress states. In-plane strains were measured during the tests. The rock stratum is inclined horizontally, thus the vertical and horizontal stresses acted in the beddings can be recognized as the major and intermediate principal stresses. Consequently, the measured strains at each of the point are the major and moderate principal strains under the condition the deformation is pure elastic. Utilizing formula (1), the principal stresses, sigma 1 and 2, can be given ... 

When the size of the plastic zone becomes nearly equal to the thickness of the specimen, plain strain conditions do not exist any more. In the plain strain condition, the plane of fracture instability is normal to the axis of the principal tensile stress. There is zero strain in the direction normal to both the axis of applied tensile stress and the direction of crack growth. The crack propagates in a direction perpendicular to the tensile stress (Stage 2). A shear decohesion also contributes to crack propagation [104]. 

This normal stress must operate in order to maintain plain strain conditions. Problem 2.8.1 Show that... 

Fig. 6.24 Notch root strain reduction consequent the passage from a plain stress (uniaxial) to a plain strain condition (multiaxial)...

Hertz stress and the consequent increase in maximum stress of around 34% is clearly visible It may be noted that, in calculating the von Mises stress, plain strain conditions have been assumed and the transverse stress, assessed using a value of Poisson s ratio of 0.28, has been included in the calculation. 

Equations 1 and 2 can be used to predict SCXj failure in any PE product if Y can be determined and SCG occurs under plain strain conditions. The limitations are (1) the obal stress should be less than about half the yield point at the test temperature to avoid a significant amount of macroscopic creep in the specimen, (2) the test temperature should be... 

To simulate an axial crack driven by hoop stress, we consider CL growth in plain strain conditions under constant load cr. The process b ins under conditions ... 

Stress corrosion can arise in plain carbon and low-alloy steels if critical conditions of temperature, concentration and potential in hot alkali solutions are present (see Section 2.3.3). The critical potential range for stress corrosion is shown in Fig. 2-18. This potential range corresponds to the active/passive transition. Theoretically, anodic protection as well as cathodic protection would be possible (see Section 2.4) however, in the active condition, noticeable negligible dissolution of the steel occurs due to the formation of FeO ions. Therefore, the anodic protection method was chosen for protecting a water electrolysis plant operating with caustic potash solution against stress corrosion [30]. The protection current was provided by the electrolytic cells of the plant. 

The literature contains many references to the use of notched, as opposed to pre-cracked or plain, specimens in laboratory studies of stress corrosion, for reasons of improved reproducibility, inability to crack plain specimens under otherwise identical conditions or ease of measuring some parameter such as crack growth rate when the crack location is predetermined. However, the developments in fracture mechanics (see Section 8.9), have resulted in a whole new field of stress-corrosion testing involving the use of specimens... 

Fig. 8.98 Threshold stress intensities from pre-cracked specimen tests, and threshold stresses from plain specimen tests, for a Mg-7A1 alloy in various structural conditions tested in chromate-chloride solution (after Wearmouth ei al )...

Conditions inside pits are complicated by the aggregation of hydrous oxides and the effect of tensile stress, which increases the dissolution velocity (per unit area) at the tip over that of a plain sheet of metal. A zeroth approximation for the electrochemistry of corrosion in a pit is to take the hemispherical tip as anodic... 

In case of applying the PLCM, the stress occurred both in a-a and d-d cross sections shown in Fig. 2, was reduced. Stress reduction is more effective in d-d cross section than in a-a cross section. Furthermore, the thicker the PLCM layer is, the more effective the stress reduction. This is because PLCM has a smaller elastic modulus than ordinary plain cement mortar, and also has a smaller thermal conductivity, which is effective to insulate the external heat through the tile at the d-d cross section. The authors gave PLCM a drying shrinkage 3 times as large as the ordinary plain cement mortar. The reduction of stress was not observed with PLCM as under cold to heat condition. On the contrary, there was a stress increase in d-d cross section. The thicker the PLCM layer is, the larger the stress increase. 

The terms semikilled, rimmed, and capped refer to many carbon steels that have been partially deoxidized or not deoxidized at all. Examples include ASTM A53 and API 5L [10] for pipe and ASTM A36, a structural steel specification. (While these specifications do no require a killing practice, some, such as API 5L, are normally supplied in the killed condition). Although plain carbon steels are often permitted in benign services such as chemically treated utility water or air lines, killed carbon steels are generally used for at least three reasons (1) There is virtually no cost difference between the two steels. The killed carbon steel is usually preferred because of its lower defect density and higher maximum code-allowable stress at higher service temperatures. 

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