Zmęczenie i Tłumienie w Prętach Pryzmatycznych
time the process of «recovery», consisting in spontaneous suppression of damages, occurs in the material. Denoting by h the rate of that process, Eq. (1.2) is obtained from the balance of the existing damages. The theoretical formula for velocity h is given on page 212; from the scarce experimental data the value AU xJ 6000 cal/mole is obtained for certain types of carbon steel. The injuries, caused by the load per unit time, %, are to be evaluated as the sum of absolute values of significant permanent strains, according to the proposal of the author . The material may be treated a theoretically as a Bingham material with the elastic limit OE and viscosity p. The Eq. (2.5) is the equation of state for such a material in one-dimensional problems. ff the load cycles are short, the value of t may be evaluated from Eq. (2.6). Permanent strains εp depend on the viscosity, which is a characteristic property of fluids. As crystals are not viscous, it is evident that the flow of a solid is caused by the growth of new amorphous phase, which accompanies the crystalline phase. This process may be treated as an endothermic process proceeding at a certain rate. If the latter is commensurable with the rate of growth of the external loads, conspicuous growth of the elastic limit σE may be expected. In this paper it is assumed that the speed of growth of the external loads is small enough (in relation to the velocity of the reaction mentioned) to neglect the changes of σE. The viscosity of the conglomerate of crystalline and amorphous phases is given by Eq. (3.3). The proper value of the activation energy is evaluated from the Hess Law, as the difference between the internal energies of both phases. The process of damping, treated in Sec. 4, is strictly connected with the increase of the temperature of the specimen. Damping is defined as the work of internal friction (the work of the stresses on permanent strains) attached to unit volume and time. Eq. (4.4) follows from the heat and energy balance where 9 is the reduced temperature difference and S the characteristic stress. There are two cases of damping curves (Fig. 3); if the dimensionless number M defined by the Eq. (4.7) exceeds e (the e basis of natural logarithms), damping stabilizes in the course of the loading process. In other cases damping grows infinitely in a finite period of time. To evaluate the defect (Sec. 5), we must take into consideration the surface fibres of the specimen
(the surface layer), because of the influence of micronotches and «self-equilibrant» stresses, caused by machining and heat treatment of various kinds. These influences are taken into account by means
of special function Zp; examples of such functions together with the «damping function» Zw are given in Sec. 7. Thus, the property is defined by Eq. (5.3) whereas Eq. (5.4) describes the dependency of the defect D on time and temperature. This equation should be solved together with Eq. (4.4). The result are the lines D = const and the Wöhler curve (D = 1). Special cases are analysed in Sec. 6; the results enable us to construct the D-(n/N)-diagrams, which are particularly useful for sequential loads. The «self-quilibrated» stresses vary with time in the course of the process of loading. The analysis of this very complicated phenomenon is given in Sec. 8. The results are rather of a qualitative character. Since fatigue and damping processes are very much influenced by heat transfer phenomena, this problem is investigated in Sec. 9. Sec. 10 deals with the confrontation of the theory with the experiments. Fig. 13a gives an experimental S-N diagram with constant of lines damping for mild carbon steel, obtained by LAZAN and Wu (Ref. , ). Fig. 13 shows the theoretical curves computed by the author. The theory is also confronted with other experiments, which deal with damping properties of various materials. Several important physical data for metals and alloys are obtained on this ground. These investigations show (in agreement with the experiments) that the specific damping capacity depends on the frequency.
J. FRENKEL, Wstęp do teorii metali, PWT Warszawa 1955.
J. MADEJSKI, Theory of Non-Stationary Plasticity, Arch Mech Stos., w druku.
B. M. ROWINSKI i W. G. LUTCAU, Izw. AN SSSR, OTN, 10, 1953, 1471.
D. S. CLARK, Metal Progress, 5, 64 (1953), s. 67.
A. EUCKEN, Lehrbuch der chemischen Physik, 2. wvd. t. 2, Leipzig 1944.
Kalendarz chemiczny, Cz. I, PWT Warszawa 1954.
A. M. FREUDENTHAL, Inelastisches Verhalten von Werkstoffen, VEB.-Verlag, Berlin 1955.
W. MOSZYŃSKI, Wytrzymałość zmęczeniowa części maszynowych, PWT Warszawa 1954.
M. A. MINER, Comulative Damage in Fatigue, Trans. ASME, 67, 1945, s. A-159.
B. F. LANGER, Fatigue Failure from Stress Cycles of Varying Amplitude, Trans. ASME, 59. (1957), s. A-160.
S. M. MARCO, W. L. STARKEY, A Concept of Fatigue Damage, Trans. ASME, 76 (1954), s. 627.
D. L. HENRY, A Theory of Fatigue-Damage Accumulation in Steel, Trans. ASME, 77 (1955), s. 913.
First Report on Viscosity and Plasticity, 2nd Ed., Amsterdam 1939.
G. A. ETEMAD, Free Convection Heat Transfer from a Rotating Horizontal Cylinder to Ambient Air with Interferometric Study of Flow, Trans. ASME, 77 (1955), S. 1283.
HARRY MAJORS Jr., Dynamic Properties of Modular Cast Iron, Part 1, Trans. ASME, 74 (1952), s. 365.
B. J. LAZAN T. Wu, Damping, Elasticity and Dynamic Stress-Strain Properties of Mild Steel, Proc. ASTM, 51 (1951).
B. J. LAZAN i DEMER, Damping, Elasticity and Fatigue Properties of Temperature Resistant Materials, Proc. ASTM, 51 (1951).
R. I. SINNOTT, I. A. ROHRIG, J. W. FREEMAN i A. J. RUSH, Carbon-Molybdenum Steel Steam Pipe After 100,000 Hours of Service, Trans. ASME, 77 (1955), S. 779.
F. R. LARSON i J. MILLER, A Time-Temperature Relationship for Rupture and Creep Stresses, Trans. ASME, 74 (1952), s. 765.
L. F. COFFIN, A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal, Trans. ASME, 76 (1954), S, 931.
HARRY MAJORS, Unpublished Report an Torsional Fatigue under a Low Number of Stress Reversais, Engineering Experiment Station, University of Alabama, University, Ala.; dane z tego sprawozdania przytoczył jego autor w dyskusji nad praca .
J. MADEJSKI, Pewne podstawowe zagadnienia dynamicznej teorii plastyczności, ref. na Zjeździe
ZMOC IPPT PAN, 1954.
J. MADEJSKI, O pełzaniu i pełzarce, Rozpr. Inzyn., 1, 4 (1956).
J. MADEJSKI, Wyboczenie pręta pryzmatycznego jako zagadnienie dynamicznej teorii plastyczności, Rozpr. Inzyn., 3, 4 (1956).
J. MADEJSKI, Zaprawa, opóźnienie sprężyste naprężenia resztkowe w ujęciu dynamicznej
teorii plastyczności, Rozpr. Inzyn., 4, 5 (1957).
J. MADEJSKI, Teoria podobieństwa zjawisk termoelastoplastycznych, Rozpr. Inzyn., 4,5 (1957).
J. MADEJSKI, Dynamiczna teoria plastyczności jako pomost miedzy teorii sprężystości a teorii
plastyczności, Rozpr. Inzyn., 1. 6 (1958),
O. FÖPPL, The Practical Importance of the Damping Capacity of Metals, Especially Steels, J. Iron Steel Inst., vol. 134, 1936, 393.
0. FÖPPL, Die Dämpfung, die bei der Schwingungsbeansptuchung von Metallen auftritt, in
Abhängigkeit von der Verformungsgecshwindigkeit, Verhandlungen des 2. Int. Kongresses für
Techn. Mechanik, Zürich 1926, 382.
W.C. HAGEL, i J.W. CLARK, The Specific Damping Energy of Fixed Beam Specimens, Trans. ASME, vol. 79, 1953, 426.