Deformation and failure of thin plate structures under blast loading

Abstract

The blast behavior and response of thin aluminum plates were investigated experimentally in this article and the results subjected to large-scale explosions in varied masses were presented. A device designed for measuring permanent deformation was used in the tests. Three types of failure were observed. The outcome was that all plates exhibited a counterintuitive behavior with distinct plastic deformation. Beyond that, some panels torn out from the boundaries. It is shown that the plates in field scale with lower blasting loading deformed similarly to those uniformly loaded in lab scale, but performed a deformation mode as localized loaded in small scale with the charge mass increased. Following that, results from experiments were used to verify the empirical formula derived before, where the yield stress of material was replaced by a novel parameter. Reasonable agreement between the predictions and the actual deflections of plates with lower impulsive loading was observed. In addition, a fitted prediction was given, which could be used to evaluate the permanent deflection in engineering calculation. The results obtained from experiments are helpful to give an insight into the differences on blast behavior between the field and lab scales.

Introduction

In recent decades, despite the practice of multiple standards in the high-technology product industry, there is a threat on military and civilian engineering structures from terrorist activities and military actions; thus, there have been concerted efforts gone into improving the capability of structures subjected to blast loading. ¹ Since such engineering structures undergoing impulsive loading are partially made of aluminum alloy plates, it has been widely assumed significant to investigate the behavior of components exposed to explosions.

Studies performed on dynamic behavior initially focused on panels made of mild steel, which could be idealized as rigid perfectly plastic. In view of describing the deformation and failure in the lab-scale tests, Nurick and Martin^2,3 derived an empirical formula for predicting the permanent deformation of uniformly loaded plates with varied boundary conditions, where the non-dimensional analysis was used to collapse the experimental results. The formula has been verified to be in good agreement with experimental results in the following investigations on mild steel plates.^4,5 Furthermore, Olson and co-authors ⁶ investigated the deformation of clamped square mild steel plates to uniform blast loading numerically and experimentally. The prediction criteria for different failure modes were presented. Nurick and Shave ⁷ carried out an experimental research on the failure modes of the strain rate-sensitive clamped plates, three modes (Mode I: large ductile, Mode II: tensile-tearing and deformation, Mode III: transverse shear) were observed, which were similar to the definition for the failure of blast-loaded clamped beams first proposed by Menkes and Opat. ⁸ Moreover, Rudrapatna et al. ⁹ presented numerical results of thin steel plates subjected to blast loading based on finite element formulation and at the same time confirmed the importance of the interaction effects of tensile and bending strain on evaluating the tearing and shearing failure.

However, due to high cost and low practicality, experiments in full-scale conducted on investigations of blast behavior are still scare. Jacinto et al. ¹⁰ provided results from large-scale experiments on steel plates, where the impulsive loading was created by detonating charges in a range of equivalent masses (from 0.8 to 10 kg) at different stand-off distances varying from 30 to 60 m. This observation reinforced the influence of boundary conditions on blast behavior. In addition, Yuen et al. ⁴ conducted a series of large-scale field tests on clamped mild steel plates and thereby concluded based on results that the deformation caused by complex loading could be approximately simplified as plates loaded uniformly in lab-scale tests. It contributes to evaluating final deflection of thin ductile plates in this article.

Commencing from the previous researches, the results of lab-scale tests for mild steel plate have been reported. However, to the author’s knowledge, there is still dearth of studies on the blast performance of plates in other materials, especially the aluminum alloy. This has led to growing interest in the field. Hence, Langdon et al. ¹¹ advocated the influence of material properties on the response of plates driven by a set of lab-scale tests, offering an understanding to the experimental investigation of the failure of four typical materials (mild steel, armor steel, aluminum alloy, and fiber-reinforced polymer composite). A novel parameter, specific energy to fracture (SETF), was proposed to compare differences on the rupture performance of materials mentioned before. Although SETF showed apparent correlation with non-dimensional impulse on the basis of test results, a wider range of data are in need to verify whether it is a definite indicator for assessment of the rupture performance. Similarly, further attempts by Aune et al. ¹² and Curry and Langdon ¹³ have been done on the structural response of thin ductile plates, where 3D Digital Image Correlation system managed to measure the transient displacement during the duration of loading. These studies revealed the mechanism of thin aluminum panels to lab-scale blast loading.

With insufficient attention paid in the literature on large-scale tests of thin aluminum panels, a series of tests with varied loading and material parameters were performed in order to provide more data. The plates were made of aluminum alloy sheets in two different thicknesses with air-blast loading arising from detonations of explosive. The permanent deflection of panels was recorded for investigating the correlation between permanent deformation and loading parameters concerned rather than transient behavior in duration of impulsive loading, the reason of which lies in the limitation of present measurements reported by Curry and Langdon. ¹³ In this article, empirical formula and a novel parameter for characterizing the material properties were utilized with an effort to compare the behavior and deformation of aluminum sheets in different conditions and predicting the permanent deflection. What should be noted is that this study has examined only structural response of aluminum plates in large scale.

Experimental study

Materials and test specimens

The specimens in 2 and 3 mm thickness utilized in field tests were manufactured using aluminum alloy sheets with an exposed area of 1200 mm × 1000 mm. The plates were then divided into three groups for blast testing (Test-A, Test-B, and Test-C) and numbered as N-TS to make a distinction, where N denotes the test number of A, B, and C, and, T is on behalf of the thickness of plates, S signifies serial number of specimens. Details of specimens are given in Table 1.

Table 1.

Details of specimens in blast testing and experimental setup.

Test	ω (kg)	ID	h (mm)	r (m)
A	1.83	A-21	2	10
		A-22	2	7
		A-33	3	7
		A-34	3	7
B	16.63	B-21	2	15
		B-22	2	15
		B-33	3	15
C	31.61	C-21	2	15
		C-22	2	15
		C-33	3	15
		C-34	3	15

The material chosen for blast tests is widely used in engineering structures, where a mass of investigations on material properties were performed. Thus, no extra quasi-static test on LY12 sheets was carried out as a result of the agreement among previous researches. The quasi-static material properties of LY12 reported by the producer were applied in this study. Table 2 illustrates the nominal chemical composition of the material. Besides, a summary of the properties is listed in Table 3, while the nominal ultimate tensile and yield strengths were provided by manufacturer to be 325 and 472 MPa, respectively. It exhibited little ductility with elongation to failure of 13%, where a novel parameter proposed by Langdon et al. ¹¹ was hereby calculated, with a SETF of 61 MJ/m³ approximately.

Table 2.

Chemical composition of LY12 (in wt%).

Si	Fe	Cu	Mn	Mg	Ni	Zn	Ti	Al
0.500	0.500	4.200	0.600	1.500	0.010	0.300	0.150	Rest

Table 3.

Material properties.

Material	Density ρ (kg/m3)	Yield stress ${\sigma }_0$ (MPa)	Ultimate tensile strength (MPa)	Ductility (% elongation to failure)	Specific energy to fracture (MJ/m3)
LY12	2780	325	472	13	61

Where ω indicates the equivalent mass of the explosion, h signifies the thickness of the plate, and r is the measured stand-off distance from location of explosion.

Experimental arrangement

Three series of experiments with the purpose of identifying the influence of loading parameters on blast behavior were conducted to specimens outdoors, where impulsive loading was generated by detonating the warhead raised off of the floor to the mid-height of the plates. The mid-height of the panels was approximately 1.5 m up the ground, which may be errors within a few centimeters but acceptable in contrast with the value of stand-off distance. As for the specimens, they were located in a circle around the explosion of each test with varied radiuses. Test-B and Test-C involved same stand-off distance of 15 m, but with different equivalent charge masses: 16.63 kg (Test-B, equivalent TNT mass) and 31.61 kg (Test-C, equivalent TNT mass). The least massive explosive of 1.83 kg was employed in Test-A, where two stand-off distances of 7 and 10 m were used. The experimental setup is shown in Figure 1.

Figure 1.

Experimental setup of each test.

The frame of the fixture was made of channel steel. To prevent from translating and rotating during blast testing, the fixture was fastened to the floor by steel chisels of 0.5 m. The testing plates of aluminum alloy were bolted to the supporting fixture. In addition, level bar was utilized to keep the plates vertical to the floor during installation. Figure 2 shows the structure after installation.

Figure 2.

Photograph of test structure after installation.

Deformation measurement

As shown in Figure 2, the front surface of each test plate was painted with grid pattern (100 mm × 100 mm) for measuring the final deformation subjected to blast loading. Moreover, a right-handed coordinate system was set to facilitate data recording. That is, if the plate deforms to the direction opposite to the impulse loading, the deflection is positive; otherwise, it is negative. The device shown in Figure 3 was designed specifically to measure the displacement in such conditions, which is composed of braced frame, level bar, depth gage, and slides. Here, the height of braced frame could be adjusted up and down for different requirements. Level bar was utilized to ensure the brace frame and specimen with the relative position of the accurate during assembly. Slides along x direction were assembled on the braced frame and slide y amounted through slide x could move along the guide track, which could ensure the measurement for deflection of any point on the plate. What is more, the precision of the depth gage used in device is 0.01 mm.

Figure 3.

Photograph showing the device for deflection measurement.

Blast test results

Determination of the blast loading

As confirmed in previous investigations,^4,10 the deformation mode of thin panels in large-scale test showed more similarities with those subjected to uniform load in lab scale as the stand-off distance increased. Thus, in view of the propagation of blast wave in such conditions, each aluminum plate could be considered as uniformly loaded. For typical exterior load originate from the explosive, it combines a positive phase followed by a negative phase. Although the mechanism how the structural response affected by each phase is still uncertain, it is generally accepted that the positive phase contributes to the permanent deformation and the negative phase seems to dominate vibration behavior during structural response.^14–17 Thus, the negative phase is neglected here due to preliminary focus on failure modes in this article.

Since equations (1) and (2) ¹⁸ derived by scaling laws have been confirmed to be valid for engineering calculation of blast parameters, they were utilized for calculating the blast-wave parameters of three tests, with scale distance $\overline{r}$ , peak positive incident overpressure $\Delta P_m$ , specific impulse of positive phase $i_{+}$ for typical pressure curves. The calculation is given in Table 4

$$\mathrm{\Delta }{P}_m=\{\begin{array}{c}\frac{1.379}{\overline{r}}+\frac{0.543}{{\overline{r}}^2}-\frac{0.035}{{\overline{r}}^3}+\frac{0.006}{{\overline{r}}^4}0.05\le \overline{r}\le 0.3\hfill \\ \multicolumn{1}{c}{\frac{0.607}{\overline{r}}-\frac{0.032}{{\overline{r}}^2}+\frac{0.209}{{\overline{r}}^3}0.3\le \overline{r}\le 1}\\ \multicolumn{1}{c}{\frac{0.065}{\overline{r}}+\frac{0.397}{{\overline{r}}^2}+\frac{0.322}{{\overline{r}}^3}1\le \overline{r}\le 10}\end{array}$$

(1)

$$i_{+}=220\frac{\sqrt[3]{{\omega }^2}}{r}$$

(2)

where $\overline{r}=r/\sqrt[3]{\omega }$ , r is the measured stand-off distance from location of explosion, and ω indicates the equivalent mass of explosion.

where $\overline{r}$ is the scale distance, $\Delta P_m$ indicates the peak incident overpressure of the positive phase, $i_{+}$ denotes the specific impulse of positive phase, and ${\delta }_{\max }$ is maximum permanent deflection of the plate. The area of the panel $S=1.2{\mathrm{m}}^2$ .

Table 4.

Summary of the blast results from three tests.

Test	ID	r (m)	$\overline{r}$ ( $\mathrm{m}/\mathrm{k}{\mathrm{g}}^{1/3}$ )	$\mathrm{\Delta }{P}_m$ (MPa)	$i_{+}$ ( $\mathrm{N}\mathrm{s}/{\mathrm{m}}^2$ )	$I_{+}=S·i_{+}$ ( $\mathrm{N}\mathrm{s}$ )	${\delta }_{\max }$ (mm)
A	A-21	10	8.170	0.015	32.939	39.526	–
	A-22	7	5.719	0.026	47.055	56.466	14.60
	A-33	7	5.719	0.026	47.055	56.466	9.26
	A-34	7	5.719	0.026	47.055	56.466	10.82
B	B-21	15	5.876	0.025	95.564	114.677	27.31
	B-22	15	5.876	0.025	95.564	114.677	26.67
	B-33	15	5.876	0.025	95.564	114.677	18.47
C	C-21	15	4.744	0.035	146.621	175.945	187.98 TORN
	C-22	15	4.744	0.035	146.621	175.945	493.97 TORN
	C-33	15	4.744	0.035	146.621	175.945	95.35
	C-34	15	4.744	0.035	146.621	175.945	89.01

Description of deformation

It should be noted that the effects of fragmentation damage observed were not considered in the measurement of permanent deflection herein and not included in the analysis of experimental data in aim of investigating the blast behavior of selected plates. With regard to failure mode, previous studies on deformation of clamped beams ¹⁹ and plates^7,20,21 identified three damage modes, that is, large inelastic deformation (Mode I), tensile tearing at supports (Mode II), and transverse shear at supports (Mode III). Furthermore, the phase of Mode I could be subdivided as Mode I (no visible necking at the boundary), Mode Ia (necking around part of the boundary), and Mode Ib (necking around the entire boundary). Except for the holes, the plates from Test-A and Test-B and the panels in 3-mm-thick from Test-C exhibited plastic deformation without any rupture or crack on front surface, which can be identified as Mode I. It was observed that the permanent displacement increased as the impulse increased and the thickness decreased, as expected. The phenomena shown in Figure 4 should be highlighted that the plates of C-21 and C-22 were torn out from the clamping frame along the bottom boundary, which performed a characteristic of Mode II.

Figure 4.

Photographs of plates from Test-C: (a) C-21, (b) C-22, (c) C-33, and (d) C-34.

Considering the structural response, there are three categories (types I, II, and III) to connect the impulsive loading and direction of deformation likewise. ²² When the components of structure vibrate on both sides of original configuration with a positive permanent displacement, it is called type I. With the increased loading, the structural component will vibrate only on the positive side, which is summarized as type II. In addition, if the component deforms to the negative side of the initial position, it belongs to type III. As shown in Figure 4, the phase of type III was found that all plates in the experiments deformed to the negative side of the original configuration, that is, in the direction opposite to the impulse loading. This phenomenon was named as counterintuitive behavior (CIB) by Symonds and Yu. ¹⁹

The results on permanent deflection of each aluminum plate from three air-blast tests were recorded, except for the slightly deformed plate of A-21, which was not included in the analysis of deformation. As a result of the performance on CIB of all the plates, the deflections recorded were positive. The maximum permanent displacement ${\delta }_{\max }$ of each plate was analogously utilized to compare the damage in different conditions, as the mid-point displacement was usually adopted as an indicator of the response to blast loading in lab-scale tests. Table 4 notes the index ${\delta }_{\max }$ of each plate. Since the plates of C-21 and C-22 are torn out from the clamping frame, it was difficult to identify the actual maximum permanent deflection of the plate in the mode of torn. Especially, C-22 exhibited a severe failure cocking from the edge. Hence, the approximate deflections of torn plates were listed in Table 4 to give a direct comparison between the deformation modes. With the fact that it was difficult to list the deflection of each sampling point from the specimens, the data were imported into MATLAB to make interpolation and surface rendering. Figure 5 shows the results of selected plates after blast loaded.

Figure 5.

Results of selected plates after surface rendering: (a) A-22, (b) A-34, (c) B-21, (d) B-33, (e) C-21, and (f) C-34.

As shown in Figure 5, the location of the maximum deflection for each plate ranged a lot. Only the panels of the C-33 and C-34 exhibited a perfect deformation shape that the maximum deformation appeared at the central area of the panels. In addition, plastic hinges along the diagonals of the plates were distinct in Test-C with the largest explosion mass, but not visible in other two tests (Test-A and Test-B) for the little deformation relative to the size of the plates. As presented in Figure 6, the maximum permanent deflections from all data points of each plate along horizontal positions were extracted and summarized to align and plot together, where the results of the plates with tearing damage are not involved. Meanwhile, the graph revealed that most plates under lower impulse loading in such scale presented the similar deformation shape with those uniformly loaded in lab scale (defined as Mode I-A in this study), which was in consistence with the previous investigations.^4,7,10 However, as loading impulse increased, the plates deformed similarly to those under localized loading in lab scale, with an obvious peak deflection in the center of the plates (classified as Mode I-B in this study). To compare directly, typical photographs of lab-scale tests were selected from former investigations.^7,23 Figures 7 and 8 present the failure of the plates subjected to uniform and localized loading, respectively, where the modes mentioned before could be intuitively observed.

Figure 6.

Maximum permanent deflection along horizontal position of typical plates.

Figure 7.

Photographs showing the failure of uniformly loaded square plates with increasing impulse in lab scale. ⁷ L/B = 1 in order of increasing impulse from left to right (16.6, 20.0, 20.2, 23.6, 24.4, and 31.2 N s). Plate thickness of 1.6 mm. Test area of 89 mm × 89 mm.

Figure 8.

Photographs of cross-sectional profiles from quadrangular plates subjected to localized loading. ²³ L/B = 2.3 in order of increasing impulse from bottom to top (8.2, 8.6, 8.9, 9.4, and 10.7 N s). Plate thickness of 1.6 mm. Test area of 290 mm × 129 mm.

Discussion

As provided in equation (3), an expression for comparing different geometries and material properties was modified by Nurick and Martin, ² where I is the impulse of blast wave; h, B, and L denote the thickness, breadth, and length of plate, respectively; ρ and σ indicate the density and quasi-static yield stress of material, respectively. It was convinced as a significant calculation of non-dimensional impulse parameter for predicting the deflection of quadrangular plates (Figure 9). Then the equation of the best fitting line obtained after plotting the displacement-thickness ratios versus the non-dimensional impulse parameter was derived as shown in equation (4). The accuracy of this prediction is corroborated by various studies concentrating on materials that could be idealized as rigid perfectly plastic,^4,6,7,9 but with a limitation in generalizing to other materials, especially to ductile and brittle materials. ¹¹ However, it could be overcame using SETF, which incorporates strength and ductility, rather than quasi-statistic yield stress proposed by Langdon et al. ¹¹ after conducting a series of investigations in lab scale. SETF is a useful parameter and provides a measure of energy without making any assumptions regarding the strain hardening, even for materials, which do not exhibit membrane behavior. It shows better correlation than material strength or ductility alone. Namely, the non-dimensional rupture impulse increased with increasing SETF. However, to author’s knowledge, further studies in field scale have not been reported to evaluate whether the finding could be apply to predict permanent deflection of CIB.

$${\phi }_q=\frac{I}{2h^2{\left(\mathrm{BL}\rho \sigma \right)}^{1/2}}$$

(3)

$$\frac{\delta }{h}=0.471{\phi }_q+0.001$$

(4)

Figure 9.

Graph of displacement/thickness ratio versus non-dimensional impulse with SETF: (a) results of all plates, and (b) results of the plates that deformed as Mode I-A.

The results from field tests (Test-A and Test-B) of different geometries were compared as given in Table 5. When subjected to lower loading, it is shown that the permanent maximum deflection-thickness ratio is inversely proportional to the square of thickness with the error not more than 6%. The results of Test-C were not included due to the torn behavior along the boundaries. It means that this regularity is applicable in the condition that the plate is in restraint or does not show any behavior of rupture with the addition of loaded impulse.

Table 5.

Comparison of displacement-thickness ratios in different thicknesses.

	${\mathrm{\Pi }}_{\max ,h=2\mathrm{mm}}$	${\mathrm{\Pi }}_{\max ,h=3\mathrm{mm}}$	Ratio of ${\mathrm{\Pi }}_{\max }$	Error
Test-A	6.99	3.30	2.12	−6%
Test-B	13.70	6.46	2.12	−6%

Where ${\mathrm{\Pi }}_{\max }={\delta }_{\max }/h$ , $\mathrm{ratio}\mathrm{of}{\mathrm{\Pi }}_{\max }={\mathrm{\Pi }}_{\max ,h=2\mathrm{mm}}/{\mathrm{\Pi }}_{\max ,h=3\mathrm{mm}}$ , and $\mathrm{Error}=(\mathrm{ratio}\mathrm{of}{\mathrm{\Pi }}_{\max }-2.25)/2.25$ . The value of inverse proportional ratio to the square of thickness is equal to 2.25, as the thicknesses of the plates are 2 and 3 mm, respectively.

The SETF is of the essence in terms of predicting the final deformation regardless of material types. Hence, it is utilized instead of the quasi-static yield stress for calculating the non-dimensional impulse number from equation (4). On the other hand, since it is generally accepted that the permanent deformation is mainly driven by the positive phase of the blast load, the impulse of the positive phase is considered for the calculations of non-dimensional impulse number for the sake of comparison between experimental results and predictions, which are presented in Table 6. Similarly, the results of experiments agree well with the predictions of non-dimensional equations subjected to lower loaded impulse but no longer fit under the circumstance of higher loading. The assumption seems to be accurate within a specific range, which should be determined on the basis of further studies. According to the performance observed in Figure 6, it infers that the predictions are exact in the situation that the plates deformed as Mode I-A.

Table 6.

Comparison between the experimental results and predicted displacement-thickness ratios of selected plates.

ID	${\delta }_{\max }$ (mm)	${\mathrm{\Pi }}_{\max }$	φq with SETF	Predicted ${\mathrm{\Pi }}_{\max }$	Error
A-22	14.60	6.99	15.66	7.38	−5%
A-33	9.26	3.04	6.95	3.28	−7%
A-34	10.82	3.55	6.95	3.28	8%
B-21	27.31	13.72	31.77	14.97	−8%
B-22	26.67	13.68	31.77	14.97	−9%
B-33	18.47	6.46	14.12	6.65	−3%

SETF: specific energy to fracture.

Where ${\mathrm{\Pi }}_{\max }={\delta }_{\max }/h$ and $\mathrm{Error}=({\mathrm{\Pi }}_{\max }-\mathrm{Predicted}{\mathrm{\Pi }}_{\max })/\mathrm{Predicted}{\mathrm{\Pi }}_{\max }$ .

A graph of displacement/thickness ratio versus non-dimensional impulse is shown in Figure 9(a), where the phenomenon described before is intuitively performed. Furthermore, Figure 9(b) indicates that the data of the plates that deformed as Mode I-A distribute within ±10% of displacement/thickness ratio of the trend line given in equation (4). For the non-dimensional impulse and displacement/thickness ratio of selected plates under such conditions, the relationship can be fitted by

$${\mathrm{\Pi }}_{\max }=0.438{\phi }_q$$

(5)

It could be used for the predictions of the plates under similar conditions.

For the plates performing the permanent deformation as Mode I-A, the results analyzed before suggest that SETF could be a good indicator for predicting their behavior and deformation when subjected to blast loading. While the ductility is equal to ultimate tensile strain of the material, SETF, the product of the ultimate tensile strength and ductility, can be explained as the product of the ultimate tensile strength and strain as well. It is approximately regarded as deformation energy of the material indicating the energy absorption capacity. More investigations on different material types need to be conducted to test the reliability of the outcome that the deformation energy makes sense on mechanical properties and blast-loaded behavior.

Conclusion

The behavior and permanent deformation of thin aluminum plates subjected to large-scale explosions has been experimentally investigated herein, with attention paid to the statement that explosions were detonated at various stand-off distances relative to the center point of the plates. The observation covered the permanent structural response of thin aluminum panels. Under such boundary condition and geometries, the quasi-statistic yield stress of the material could be replaced by SETF for calculating the non-dimensional impulse parameter. For the sake of establishing the relationship between non-dimensional impulse and permanent deflection, the results of deformation were recorded and plotted in non-dimensional form as displacement/thickness ratio. It is found that displacement/thickness ratio increases linearly with increasing loaded impulse when the plate performs deformation as Mode I-A. The data from a series of experiments are in deep agreement with the predictions, with the error not more than 10%. Thus, the fitted prediction could be used to evaluate the permanent deflection of similar deformation mode in engineering calculation. Moreover, with higher loaded impulse, it was observed that the plates deformed as dome with a distinct peak displacement in the center and even torn out along the boundaries, which were identified as Mode I-B and Mode II. For these plates, the prediction derived by non-dimensional analysis does not fit any more, as shown in Figure 9(a). Thus, the equation verified as a reliable prediction in lab scale is less accurate for evaluating the damage in field tests. Notwithstanding not deriving the equation for predicting the deformation of Mode I-B and Mode II with the limited specimens, this study does indicate the phenomenon differing from those of the plates in lab scale and subdivide the initial damage mode for applying the equations into large scale, which is helpful to give an insight into the difference on blast behavior between the field and lab scales. Furthermore, it is also noted that all the plates underwent a CIB as deformed in the direction opposite to the impulse loading, which defined as type III when considering the structural response. Unfortunately, we cannot determine more from these data. Both of the tearing and CIB should be further investigated and summarized.