KINETICS OF CRACK PROPAGATION UDC 539.4.42:620.18

V. N. Kuranov, V. I. Ivanov, and A. N. Ryabov

New experimental methods based on analysis of acoustic emissions and measurements of electrical potentials are being used to study the mechanics and physics of crack nucleation and propagation processes. Such studies of the static and cyclic strength of materials and structures make it possible to obtain information on processes and phenomena occurring in localized volumes of a material during crack nucleation and the development of fracture. It is well known that the recording of acoustic emissions is evidence of the radiation of energy in mlcrovolumes of a material. The impulsive emission of elastic energy occurs as a result of different dislocation processes, as well as from "instantaneous opening of an elastic body," -- a disturbance of its continuity; the newly formed surface should be free of stresses. The nonstationary process of restructuring of the stress field, occurring at a finite rate dependent on the elastic constants of the material, stimulates the appearance of elastic oscillations in the body. Detection and analysis of these oscillations are the principal elements of the method of acoustic emission. The use of such special measures as three-dimenslonal location time strobing and selecting acoustic emission signals from growing cracks according to parameters of the external load, along with continuous recording of crack length by the method of electrical potentials, make it possible to discover and eliminate the effects of sources of ambient noise and ensure that the information obtained is reliable and complete and directly related to fracture processes. Using such measurements, investigators have obtained new empirical data on fracture processes in local regions of the material near the front of a growing crack [I, 2]. In these studies, the structural strength of power-plant lines was evaluated by testing fullscale sections of these pipelines and their welds under static and pulsating loading with internal pressure. The pipes, made of steels 15KhlMIF, 12KhlMF, and 20, each had a diameter of 220 mm and wall thickness of 20-45 mm. Pipes of steel 22K (with an anticorrosive inside hard-face) tested had dimensions of 848 and 48 mm, respectively. Cracks were initiated (in the tests) on the outer surface of the pipes in the region of the base metal and at welds by machining notches of different sizes into the metal. The tests were conducted at room temperature on a base of I04 load cycles. Loading rate was about !0-~-10 -~ rel. strainunits/min (according to data from tensometric measurements). During the tests, investigators continuously eters (time of onset of event, coordinates of the of events, number of oscillations in a pulse, the the event, etc.), loading conditions, and changes of the surface cracks being measured.

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The acoustic emission equipment used in the studies (Donlgan/Endevko Company, USA, types 1032 and 3000) provided for automatic analysis of the incoming data, reproduction of the data during testing in printed form and on a display panel, and storage of data for subsequent analysis using special programs. Subsequent analysis revealed zones of crack nucleation and growth~ the moment of crack appearance, and stages of crack propagation. The kinetic characteristlcs of crack growth were analyzed in connection with the conditions of external loading. In both the present study and in [3] it was noted that the acoustic emissions recorded during the stages of crack nucleation and growth have features attributable to the different natures of the processes that generate the acoustic signals. Analysis of pulse distribution according to amplitude shows that mainly a "low-amplltude" acoustic emission is recorded in Central Scientific Research Institute of Technology and Machinery Manufacture (TsNIlTmash), Moscow. Translated from Problemy Prochnosti, No. 6, pp. 15-19, June, 1980. Original article submitted October 29, 1979.

0039-2316/80/1206-0683507.50

9 1981 Plenum Publishing Corporation

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Fig. i. Location of piezoelectric transducer (DO, DI, D2, D3) for three-dimensional location of acoustic emission from a growing surface fatigue crack on a high-pressure vessel (dashed line) and the results of the location for the entire period of crack growth and individual stages of growth (i, 2, 3, etc.). (In the rectangular coordinates, each point corresponds to an acoustic emission event associated with crack front advance.) the stress concentration zone in the period preceding appearance of the crack~ With appearance of the crack and during its growth, acoustic emissions that are more than an order greater in amplitude are recorded over the "low-amplitude" background. Since two groups of processes are known to accompany the emission of acoustic signals -plastic deformation (dislocation movement, disintegration of dislocation complexes, penetration of various types of boundaries by dislocation pile-ups, the operation of any type of dislocation source~ etc.) and elastic microscopic ruptures in the continuous material -- a characteristic acoustic emission is associated with each of these groups. Low-amplitude acoustic emission is associated with processes of plastic deformation in stress concentration zones, including crack tips, while high-amplitude emission is connected with crack propagation processes, manifest in the form of microscopic ruptures and accompanied by the creation of new crack surfaces.* Examining the features of acoustic emission makes it possible to investigate fracture processes at different stages of development in greater detail. In view of this~ we looked at several important features of crack propagation. A study of acoustic emission shows that crack tip growth is irregular: different zones of crack front advance are apparent (Fig. i) during load application. Analysis of acoustic remission within coordinates along the front under cyclic loading of a high-pressure vessel with internal pressure shows =ha= crack propagation results from local advances along the front of the crack (Fig. 2). Continuous measurements of the length of propagating cracks by *The order of the numerical values obtained for the amplitudes may differ, depending on the properties of the measurement objective, the specifications and operating conditions of the acoustic equipment and transducers, the conditions of acoustic contact, etc. However, the qualitative character of the distribution of acoustic emission with respect to amplitude remains the same. 684

Fig. 2. Acoustic emission in coordinates along fatigue crack front at different stages of crack growth. the method of electrical potential also shows that periods of growth in individual zones of the front alternate with stoppages lasting tens of load cycles. The observations showed that acoustic emission is connected with the conditions under which a crack body is loaded (the direction, magnitude, and character of change in the acting stresses in the crack propagation zone). The external loads at which acoustic signals from the front of a growing crack are received correspond to very low nominal acting stresses (3-5 kgf/mm~). In the case under consideration, cyclic loading of the high-pressure vessel of steel 15KhlMIF (diameter 250 ram, wall thickness 40 mm) produces a distribution of acoustic emission with respect to internal pressure having the character shown in Fig. 3. Worth noting is the fact that a change in the external loading conditions (in Fig. 3, a change in the maximum stress in the internal pressure cycle) does not lead to any marked change in the loads at which acoustic emissions are recorded due to crack front advance. This fact is of interest for determining the conditions of unstable crack propagation and evaluating critical values of fracture resistance characteristics in local volumes of the material at the front of cracks. Measurements of crack length by the method of electrical potential (using a 1000-Hz alternating current) revealed characteristic features of the behavior of the material in the small region near the crack tip during external load cycling. The measurements showed an "apparent" change in crack length per cycle (the sensitivity of the equipment used in the experiment was approximately in units of microamperes). Given the measurement technique used, this change can be explained by a change in the magnetic susceptibility of the material and magnetic and thermomagnetic effects sensitive to elastic and plastic strains [4]. As the numerous measurements showed, the shape of the curves and the amplitude of the apparent change in crack length are related in a definite manner to the dimensions of the crack and the loading conditions. Analysis of the curves at different stages of crack growth and with a change in cycling conditions showed that crack growth rate is related almost linearly to the change in crack growth length during the cycle (Fig. 4). This fact may be regarded as empirical confirmation of previous suggestions [5] to the effect that plastic deformation and the effects of cyclic deformation are important factors in controlling the crack propagation process. From an energy approach, the macroscopic rate of crack growth isdetermined by the propertion of work done by external forces and the sum of accumulated elastic strain energy, kinetic energy, and the energy dissipated in the small volume at the crack tip. The familiar "Jump" phenomenon in fracture toughness tests is related to the liberation of elastic energy with a macroscopically large crack advance and is used to establish limiting values of the stress intensity factor. Several orders less of energy are liberated [6] in the crack advances usually seen after one cycle of alternating loading (i0-~ mm or less). The spectrum of the oscillations generated in the fracture zone extends into the ultrasonic region. The duration of an individual acoustic signal is of the order of microseconds, while the amplitude of the mechanical displacements is i0-" m. Highly sensitive methods and equipment are needed to pick up such

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Fig. 3. Distribution of acoustic emissions from a growing fatigue crack in a high-pressure vessel with respect to internal pressure under different loading conditions. Fig. 4. Dependence of resistance to crack growth on relative value of "apparent" change in crack length in a cycle. radiations, and the method of acoustic emission affords this sensitivity. The results of recording acoustic emissions can be used to establish the moment instability is reached in local volumes of the material at the crack tip and, thus, to evaluate limiting conditions on the microstructural level. Critical values of stress intensity factor equal to about 70-80 kgf.mm -s/~ (Fig~ 5) were obtained in fracture toughness tests of specimens and models of pressure vessels made of different materials (low- and medium-strength) using the methods and relations of linear fracture mechanics (we took as the breaking load that at which an acoustic emission was noted in the case of crack advance -- see Fig. 3, for example). These values are close to the lowest values of fracture toughness seen in experiments [7]. Using the same methods and relations, we can find the dependence of macroscopic fatiguecrack growth rate on the amplitude of the stress intensity factor calculated from the maximum and minimum loads in a cycle and the loads at which acoustic emissions were recorded. This dependence can be described by a relation of a single type, but one that has different values of exponent for the amplitude of the stress intensity factor (the exponent in Eq. (2) is many times greater). Taking the above into account, the results obtained may be explained as follows. Equation (i) may to a first approximation characterize the change in the total work done by external forces, while Eq. (2) can characterize the change in the amount of accumulated elastic strain energy liberated during each crack advance. The deviation of Eq. (i) from Eq. (2) is evidence of a change in the energy ratio with a change in loading conditions (mode of loading~ crack dimensions, etc.). A more rigorous explanation could be given if the increase in the amount of new crack surface formed -- rather than the increase in the linear dimensions of the crack -- were analyzed in relation to loading conditions. The results presented here and earlier [1, 2] from experimental observation of localized phenomena in the vicinity of the tip of growing cracks allow us to advance several related proposals important in establishing the kinetics of the process of crack propagation: i) crack front advance is an irregular and discontinuous (discrete) process; 2) crack growth occurs by brittle rupture; 3) resistance to crack propatagion depends on loading history of =he crack-tip material. The fracture toughness of material damaged as a result of previous plastic deformation and cyclic strain de=ermines the conditions of the onset of local ins=ability at the crack front. 686

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Fig. 5. Dependence of resistance to crack growth on amplitude of stress intensity factor. (Solid line denotes amplitude of stress intensity factor computed from the maximum and minimum loads in a cycle, while the dashed line shows amplitude values calculated from the loads at which acoustic emission was noted.) 4) plastic deformation, strain hardening, and the effects of cyclic deformation are the factors that control =he kinetics of crack propagation. Taking the above into account, we may examine the following mechanism of crack propagation. There are residual compressive stresses present in the vicinity of the crack tip in the absence of an external load. With an increase in the latter (tensile), compression decreases, the stresses change sign, and the crack surface moves apart. Elastic strain energy in the tip region increases. Meanwhile, the previous loading has made the material less capable of plastic deformation and strain hardening. Moreover, in inhomogeneous polycrystalline materials, the remaining capacity of the material for plastic deformation and strain hardening is nonuniform in different zones near the crack front in the case of cracks of complex configuration or when the stress state along the crack front is variable. Local instability of the crack front and sudden crack advance by brittle rupture will occur a= certain values of external load (the nominal acting stresses here total 3-5 kgf/mm ~) in a crack-front zone in which the accumulated elastic strain energy exceeds the limiting value. New crack surfaces are formed and, due to rapid stress and strain redistribution in =his region, oscillations are generated (acoustic emission is observed). Crack advance in this region is arrested due to stress and strain redistribution along the crack front, and the crack may advance into adjacent zones if limiting conditions are achieved there. A flow of energy into =he fracture zone is needed to "accelerate" the crack and maintain its unstable, irregular propagation. If this is not provided by the loading conditions and if the material retains its capacity to deform plastically and straln-harden, the crack is stopped. In this case, with a further increase in the external loads, the work done by these loads is spent on plastic deformation and strain hardening of the material at the crack front. Here, conditions for crack advance may again arise in some crack-front zone (such as in the case of one-time loading of a cracked solid to the point of fracture). Removal of the external loads is accompanied by elastic unloading of the material at the crack front and a change in the sign of the stresses and plastic strains under the influence of the compressive stresses that arise. In contrast to well-known continuum models of crack propagation [5], =he above model is based on the results of empirical study of localized phenomena at the crack tip and includes part of the propagation process, where elastic strain energy is dissipated by plastic deformation and strain hardening and new crack surfaces are formed. The results presented here are in good agreement with concepts of the energy approach to fracture processes in a cracked solid and may be regarded as empirical verification of the latter.

687

Further observations for materials of different classes and cracked solids in relation to their structural features, external loading conditions~ and environment will make it possible to quantitatively analyze the relationship between the motive and dissipated energies in crack propagation and on this basis obtain a unified description of the laws of crack growth in brittle and quasibrittle solids which fracture with single or multiple application of external loads. LITERATURE CITED i.

2.

3. 4. 5. 6. 7.

V . N . Kuranov, V. I. Ivanov, S. I. Tishin, and V. S. Makarov, ~'Investigation of the laws of fatigue crack growth and fracture resistance using the methods of acoustic emission and electrical potential," in: Predicting the Strength of Long-Life Machine Materials and Structural Elements [in Russian], Naukova Dumka, Kiev (1977), pp. 192-199. V . I . Kuranov, V. I. Ivanov, and A. N. Ryabov, "Possibilities of the practical application of acoustic emission phenomena in evaluating the fracture resistance of structures with defects," in: Applied Problems of Fracture Mechanics in Machine Construction, NPO TsKTI im. I. I. Polzunova, Moscow (1977), pp. 121-123. Y. Nakamura, C. L. Veach, and B. O. McCauley, "Amplitude distribution of acoustic emission signals," Am. Soc. Test. Mater., Spat. Tech. Publ. No. 505 (1972). K . P . Belov, Elastic, Thermal, and Electrical Phenomena in Ferromagnets [in Russian], GITTL, Moscow (1957). F. Erdogan, "Theory of the propagation of cracks," in: Fracture [Russian translation], Vol. 2, Mir, Moscow (1975), pp. 521-616. V . M . Finkel', PhysicalBases of the Retardation of Fracture [in Russian], Metallurgiya, Moscow (1977). J . I . Bluhm, "Brittle fracture and its prevention," in: Fracture [Russian translation], Vol. 5, Mashinostroenie, Moscow (1977), pp. 11-69.

EFFECT OF SCALE FACTOR AND RESIDUAL WELDING STRESSES ON FATIGUE CRACK GROWTH RATE V. I. Trufyakov, P. P. Mikheev, and A. Z. Kuz'menko

UDC 539~4,013~!3

Under cyclic loading, the stages of fatigue crack growth may vary within a wide range when evaluated according to the number of cycles and may account for I0 to 90% of the total life of the product. In predicting the safe life of products, fatigue crack growth stages characterized by crack growth rate are determined in engineering practice on the basis of fracture mechanics criteria [1-6 et al.]. Initial relationships between fatigue crack growth rate and the amplitude of the stress intensity factor, described by the well-known exponential equation of Paris [6], are generally determined empirically under laboratory conditions. However, there are certain problems in directly using these relationships to calculate the time of subcritical fatigue crack growth in actual welded structures. These problems are due first of all to the fact that the role of the scale factor is not always considered in conducting base experiments. This factor~ by changing the stress--strain state at the crack tip, may (other conditions remaining the same) lead to substantial changes in crack growth rate. A second important fat=or helping to determine the stress--strain state at the crack tip is the residual stresses inherent in the formation of welds. This factor must also evidently be considered in establishing the initial relationships between crack growth rate and stress intensity factor amplitude. The present work examines the results of experimental studies of the change in the rate of growth of fatigue cracks in structural steel in connection with the scale factor and the effect of residual welding stresses. E. O. Paton Institute of Electric Welding, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Problemy Prochnosti, No. 6, pp. 20-22and 30, June, 1980. Original article submitted May 3, 1979.

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0039-2316/80/1206-0688507.50

9 1981 Plenum Publishing Corporation