Atomistic modeling of crack growth in magnesium single crystal

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AbstractMethodologyMaterial ModelInput DataResultsAcknowledgmentsReferences


The analysis of crack growth in magnesium single crystal was performed using molecular dynamics simulation with Embedded Atom Method (EAM) potentials. The twinning process at the crack tip was analyzed. Four specimens with increasing sizes were used to investigate the influences of material length scale on crack growth of magnesium single crystals. Furthermore, the effects of temperature, and the loading strain rate were also verified. The specimens were subjected to uniaxial tension strain up to the total strain level of 0.2 with a constant strain rate. In the simulation of each specimen, the averaged stress strain curve was monitored. The simulation results show that the specimen size, loading strain rate, and temperature strongly influence the peak stress point at which the twin nucleated and subsequently the crack grew. The initial slope of the averaged stress strain curve is independent of the loading strain rate and temperature. Moreover, high temperatures induce increased atomic mobility, and thereby atom reorganization, which, in turn, releases the stress at the crack tip.

Author(s): Tian Tang, Sungho Kim, Mark F. Horstemeyer, Paul Wang

Corresponding Author: T.Tang

Figure 1. Crack growth and the development of twin pattern of the specimen-1 with 4884 atoms at various applied strains. (click on the image to enlarge).
Figure 2. Influences of specimen size on the averaged stress–strain response of magnesium single crystal specimen containing a center initial crack. (click on the image to enlarge).


Background information of the EAM potential can be found here:

Figure 3. Model geometry of magnesium single crystal containing a center initial crack.

The size effects on the crack growth were studied using four specimens (from 1 through 4) of increasing size (ranging from from 4884 to 229,900 atoms) - generated by increasing the width and the height of the specimen (maintaining the thickness, t, constant). As shown on Figure 3, a center crack was introduced in each specimen by removing the atoms from the perfect crystals and maintaining the ratio of the initial crack length to the width of the specimen to a/w = 0.1. The top and bottom boundaries are free surfaces. There is about 1 nm deep atomic surface layers at the top and bottom boundaries that were fixed for applying Mode I cyclic loading. In all simulations, the specimens were equilibrated at 100 K by running 2000 timesteps before applying uniaxial tension loading. The uniaxial tension strain loading was applied along the y axis up to the total strain of ey = 20%. For the sake of eliminating the stress oscillation resulting from the sudden loading employed on the top and bottom boundary, the loading was applied such that the velocity was linearly distributed along the y-direction from the bottom to the top. Except in the investigations of strain rate effects, the uniaxial tension loading was applied at a constant strain rate of 109 Hz. All simulations were performed at a constant temperature of 100 K except in the studies of the effects of temperature.

Material Model

Input Data


Figure 4. The atomic structure of twin at the crack tip at various externally applied strains.

The MD simulations of crack growth in magnesium single crystals using EAM potential at the nanoscale were performed. The twinning process at the crack tip can be observed on Figure 1 and 4. The influences of specimen size on the stress-strain curve is shown on Figure 2. The strain rate and temperature dependence, as well as the calculated fracture toughness, are presented on Figure 5, 7, 7.

According to the simulation results, the following conclusions were obtained:

  • The atomic structure of the matrix material was almost unaffected by the nucleation and growth of twin bands from the crack tip.
  • The significant size effects were clearly demonstrated by averaged stress–strain responses. The peak stress point decreases with increasing specimen size. The initial slope of the average stress strain curve is independent of the specimen size except the smallest specimen size. Meanwhile, it is also found out that the size effects decrease with increasing specimen size. The fracture toughness increased with increasing specimen size when maintaining the size proportions of the specimens.
  • Furthermore, the peak stress point decreased with increasing strain rate, initial crack length, and temperature. On the other hand, the initial slopes of average stress strain curves are independent of strain rate and temperature. The twinning becomes weak and the material becomes ductile at high temperature so that the resistance of crack growth increases with increasing temperature. This effect results from the stress at the crack tip being released by the reorganization of atoms due to the high mobility of atoms at high temperature.
  • In all loading conditions and specimen sizes, the decrease of averaged stress–strain response is mainly due to the nucleation of twinning at the crack tip followed by the crack starting propagation.
Fig.5. Variation of fracture toughness with the normalized specimen sizes.
Fig.6. Effects of strain rate on the averaged stress–strain response of magnesium single crystal specimen containing a center initial crack.
Fig.7. Temperature effects on the averaged stress–strain response of magnesium single crystal specimen containing a center initial crack.


The authors acknowledge the Center for Advanced Vehicular Systems at Mississippi State University and the Department of Energy for supporting this research.


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