International Journal of Metalcasting

, Volume 13, Issue 1, pp 146–157 | Cite as

Research on Dynamic Accumulation Effect and Constitutive Model of Aluminum Foams Under Dynamic Impact

  • Hua Gao
  • Chao XiongEmail author
  • Junhui Yin
  • Huiyong Deng


Aluminum foams were prepared by melt foaming process. The mechanical properties of aluminum foams under repeated impacts were studied. The porosity and pore size of the prepared aluminum foam were measured. The effects of damage accumulation on the failure morphology of aluminum foam, the transmission rate, stress–strain curve, energy absorption capacity, and the ideal energy absorption efficiency were analyzed. The influence of the number of impacts on the dynamic mechanical properties of the material under the condition of equivalent damage accumulation was studied. Based on the Sherwood–Frost equation, the damage cumulative constitutive model of the aluminum foams under repeated impacts was established. The influence of the difference between the damage cumulative energy corresponding to the reference curve of the shape function and the damage cumulative energy in multiple impacts tests on the prediction accuracy of the constitutive model was analyzed. The results show that with the increase in the number of impacts, the degree of damage to aluminum foam increases, transmission rate increases, the elastic limit stress and the corresponding strain are enhanced, and the damage accumulation effect on aluminum foam under repeated impacts is helpful to improve the ideal energy absorption efficiency. It is verified that the constitutive model can reflect the mechanical properties of aluminum foam under repeated impacts.


aluminum foams dynamic compression energy absorption efficiency damage accumulation constitutive model 

List of symbols

\( \bar{D} \)

Average pore size

\( X_{D} \)

Pore size probability

\( K \)



Cross-sectional area of the bar


Wave velocity


Elastic modulus

\( L_{\text{s}} \)

Thickness of samples

\( A_{\text{s}} \)

Cross-sectional area of samples

\( \varepsilon_{i} \left( t \right) \)

Strain on the incident bar

\( \varepsilon_{t} \left( t \right) \)

Strain on the transmitted bar

\( W_{i} \)

Energy of incident wave from the beginning to the unloading

\( \sigma_{i} \)

Incident wave stress

\( T \)

The time from loading to unloading

\( \dot{\varepsilon } \)

Strain rate

\( \sigma_{\hbox{max} } \)

Maximum stress on the stress–strain curve in the strain range of 0–\( \varepsilon \)


Ideal energy absorption efficiency

\( T_{\text{m}} \)

Temperature of the test environment

\( \rho \)

Density of the material

\( H\left( {T_{\text{m}} } \right) \)

Temperature influence function

\( G\left( \rho \right) \)

Density function

\( M\left( {\varepsilon ,\dot{\varepsilon }} \right) \)

The strain rate enhancement

\( f\left( \varepsilon \right) \)

Shape function

\( N\left( {W,\dot{\varepsilon }} \right) \)

Elastic ultimate stress under different initial impact conditions

\( W_{m}^{n} \)

The sum of the initial impact to the nth impact incident energy under the condition that the initial impact velocity is m

\( a_{m} \), \( b_{m} \), \( c_{m} \)

The corresponding fitting parameters

\( \sigma_{0} \)

The elastic ultimate stress corresponding to the reference curve

\( q \)

The number of terms expanded by the power series

\( E_{p} \)

The fitting parameter to the reference curve

\( E_{j} \)

The absolute value of the difference between the damage cumulative energy corresponding to the reference curve of the shape function and the damage cumulative energy in the jth impact

\( S_{j}^{2} \)

The discrepancy between the predicted curve and the experimental measured curve



The authors wish to acknowledge, with thanks, the financial support from the Army Key Research Projects. We would like to thank Ms. Gao for proofreading the paper.

Supplementary material

40962_2018_245_MOESM1_ESM.xls (56 kb)
Supplementary material 1 (XLS 56 kb)
40962_2018_245_MOESM2_ESM.xls (55 kb)
Supplementary material 2 (XLS 55 kb)
40962_2018_245_MOESM3_ESM.xls (48 kb)
Supplementary material 3 (XLS 48 kb)
40962_2018_245_MOESM4_ESM.xls (36 kb)
Supplementary material 4 (XLS 36 kb)
40962_2018_245_MOESM5_ESM.xls (34 kb)
Supplementary material 5 (XLS 34 kb)
40962_2018_245_MOESM6_ESM.xls (46 kb)
Supplementary material 6 (XLS 46 kb)


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Copyright information

© American Foundry Society 2018

Authors and Affiliations

  1. 1.Army Engineering UniversityShijiazhuangChina

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