Maximum stress and maximum unit volume energy absorption method for simplified measurement of material buffer curve

Abstract

The invention discloses a maximum stress and maximum unit volume energy absorption method for simplified measurement of a material buffer curve. The method comprises the following steps: step 1, determining a minimum value emMin and a maximum value emMax of maximum unit volume energy absorption em; step 2, dividing the maximum unit volume energy absorption em into a plurality of value points emi with approximately uniform intervals; 3, measuring to obtain a maximum stress value sigma mi corresponding to each maximum unit volume energy absorption value emi; 4, sequentially measuring ne maximum stress and maximum unit volume energy absorption type value points (emi, sigma mi); 5, constructing a relation curve of the maximum stress sigma m and the maximum unit volume energy absorption em; and step 6, constructing a [G]-sigma s buffer curve under the combination of any drop height h and liner thickness t of the buffer material by using a relational expression of the maximum stress and the maximum unit volume energy absorption. The measuring process of the [G]-sigma s buffer curve of the buffer material is simplified by constructing the relational expression between the dynamic buffer coefficient and the maximum unit volume energy absorption of the buffer material, so that the [G]-sigma s buffer curve of the buffer material under the ratio of any drop height to the liner thickness can be constructed.

Description

Technical Field

[0001] The invention belongs to the technical field of product cushioning packaging design, and in particular relates to a maximum stress and maximum unit volume energy absorption method for simplified measurement of a material cushioning curve. Background Art

[0002] During product logistics and transportation, drops and impacts can lead to product damage, resulting in significant economic losses. Only by inserting cushioning material of appropriate thickness and load-bearing area between the inner product and the outer packaging can we prevent overpacking while minimizing the risk of poor packaging. This is the key to effective product protection and effective cushioning material utilization. To effectively design cushioning packaging for products, a cushioning curve must be constructed. This curve determines the appropriate thickness and load-bearing area based on information such as the fragility and mass of the object being cushioned, as well as the equivalent drop height in the distribution environment.

[0003] At present, according to the standards "GB / T 8167-2008 Dynamic Compression Test Method for Packaging Cushioning Materials" and "ASTM D1596-2014 Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material", the buffer curve of the ratio of maximum acceleration to gravity acceleration (product brittleness value) with respect to static stress - [G]-σ s Curve, and then according to the standard "GB / T8166-2011 Cushioning Packaging Design", the [G]-σ of the cushioning material can be used s Buffer curve, design buffer packaging for products. [G]-σ s The dynamic impact test of the cushion pad on which the cushion curve is based reproduces the falling process of the product packaging. This cushion curve is the most reasonable, scientific and practical, and has become the preferred cushion curve for product cushion packaging design. The test principle diagram is shown in the figure below. Figure 1 The corresponding drop hammer impact test device includes an impact testing machine, a testing machine controller, and a data acquisition and processing system, the latter of which includes a charge amplifier, a data acquisition card, data acquisition and processing software, and a computer.

[0004] The drop hammer is equivalent to a cushioning protection product, its mass is m, and it is placed on a cushioning pad with a bearing area of ​​A. The static stress σ generated by its gravity is s satisfy

[0005] σ s =mg / A (1)

[0006] In the formula, g is the acceleration due to gravity. Assume that the deformation of the buffer pad under impact is x, the transient reaction force of the buffer pad against the impact of the drop hammer is F(x), and the initial thickness of the pad along the impact direction is t. Then the corresponding strain ε of the pad = x / t, and the strain rate Assume that the acceleration of the drop hammer is a. According to Newton's second law, there is a relational expression

[0007] F(x) = m(a + g) (2)

[0008] The stress generated by the buffer material against impact is related to ε and is defined as

[0009]

[0010] Then during the impact process, the energy absorption per unit volume e of the buffer pad is

[0011]

[0012] Assume that the velocity of the drop hammer when it contacts the buffer pad is the initial impact velocity v0. Then the equivalent drop height h of the drop hammer = v0 2 / 2g. When the impact deformation x of the buffer pad is equal to the maximum deformation x m (generally x m << h) of the buffer pad during the impact process, the kinetic energy of the drop hammer is completely converted into the deformation energy of the buffer material, that is

[0013]

[0014] In the formula, ε m is the maximum strain corresponding to x m of the buffer pad, and ε m = x m / t. Then corresponding to ε m , the maximum energy absorption per unit volume e m of the pad is

[0015]

[0016] Then, from the above formula, we can get

[0017]

[0018] When x ∈ (0, x m , that is, ε ∈ (0, ε m , the maximum value of m is the impact peak stress σ

[0019]

[0020] In the formula, [G] is the brittleness value of the product, that is, the ratio of the maximum acceleration it can withstand to g. From the above two formulas, we can get

[0021]

[0022] Define the Cushion factor C as

[0023] C=σ m / e m (10)

[0024] C is also called the buffer coefficient. According to the above two formulas, C can also be expressed as

[0025]

[0026] According to the standards "GB / T 8167-2008 Dynamic Compression Test Method for Packaging Cushioning Materials" and "ASTM D1596-2014 Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material", the cushioning material [G]-σ is measured. s The DY-2 drop hammer impact tester (produced by Xi'an Guangbo Testing Equipment Co., Ltd.) Figure 2 As shown. According to these two experimental standards, the impact tester is used to carry out a drop hammer impact test on a certain buffer material at a certain drop height and pad thickness. The cross section of the test sample along the impact direction is generally rectangular, with a length and width of not less than 100 mm or 4 inches. During the drop hammer impact test, the bottom surface of the sample is fixed to the center of the upper surface of the rigid support base, ensuring that its center is on the same vertical line as the center of the drop hammer, and its bearing surface is parallel to the bottom surface of the drop hammer. The drop hammer falls freely from the drop height and hits the sample. An acceleration sensor is installed on the drop hammer. After sampling by the data acquisition and processing system, the acceleration-time aT curve of each drop hammer impact can be obtained, from which the maximum acceleration of the impact is obtained. The same sample is impacted five times continuously, and the time interval between two adjacent impacts is 1-30 minutes. A number of the five consecutive impacts are taken, and the ratio of the average value of the maximum acceleration of the last four impacts to g is generally taken as the [G] value. According to formula (1), the weight of the drop hammer at this time is divided by the cross-sectional area of ​​the pad along the impact direction to obtain σ s By changing the configuration of the mass block on the drop weight, the mass and impact energy of the drop weight can be adjusted to obtain different maximum accelerations. At least five different mass block combinations are required to generate the final cushioning curve. In this way, a series of (σ s ,[G]) experimental value, and then use the curve fitting method to construct the final [G]-σs By making cushioning samples of different thicknesses for the cushioning material and repeating the above drop test process at different drop heights, a series of [G]-σ curves of the cushioning material can be obtained. s Buffer curve.

[0027] It can be seen from this that in order to obtain the [G]-σ of a certain buffer material s The cushioning curve must be calculated under certain drop heights and cushion thicknesses. It is difficult to enumerate all drop heights and cushion thicknesses, so the continuity of the cushioning curve with respect to drop heights and cushion thicknesses cannot be achieved. It is impossible to calculate the cushioning curve of the cushioning material under any drop height and cushion thickness within a certain range.

[0028] In order to determine the [G]-σ of a certain cushioning material under a certain drop height and cushion thickness s To obtain the cushioning curve, at least five different mass combinations are required for impact testing; the same sample must be impacted five times in succession, with a long time interval between two adjacent impacts. To obtain the [G]-σ of a certain cushioning material at different drop heights and pad thicknesses s The curve family requires a huge number of test specimens to be tested one by one at each drop height and pad thickness combination. Considering the time consumed in sample preparation, interval waiting, etc., the existing measurement of [G]-σ s It is conceivable that the buffer curve method incurs huge costs in terms of sample purchase fees, test time consumption, and equipment testing expenses.

[0029] Existing [G]-σ s The buffer curve determination method has the following problems:

[0030] (1) It can only be used for a certain combination of drop height and pad thickness, and cannot be exhaustive. It is impossible to achieve the continuity of the buffer curve with respect to the drop height and pad thickness. It is impossible to calculate the buffer curve of the buffer material under any combination of drop height and pad thickness within a certain range.

[0031] (2) For a certain drop height and cushion thickness combination, at least 5 (usually 10) drop weight impact tests should be carried out on the cushioning material sample. If [G]-σ is to be measured at different drop heights and cushion thickness combinations, s The buffer curve requires a large number of test samples, and the corresponding sample purchase and production costs are high.

[0032] (3) For each impact, the drop hammer must impact the same sample five times in succession, and a long time interval must be maintained between two adjacent impacts. The test process is complex and requires multiple repetitions.

[0033] (4) The large number of samples required requires a long time in the production, testing and waiting stages, resulting in a large total time consumption.

[0034] (5) The purchase cost of the drop hammer impact test equipment is high, and each test takes a long time, which means that the total cost of using the test equipment and determining the buffer curve is high.

[0035] In summary, it is necessary to propose an effective [G]-σ s A simplified method for determining the buffer curve can significantly reduce the amount of experiments and improve the efficiency of constructing the buffer curve. Summary of the Invention

[0036] In order to overcome the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a maximum stress and maximum unit volume energy absorption method for simplifying the measurement of the material buffer curve. By constructing a relationship between the dynamic buffer coefficient and the maximum unit volume energy absorption of the buffer material, the measurement process of the [G]-σs buffer curve of the buffer material is simplified, thereby constructing the [G]-σs buffer curve of the buffer material under any ratio of drop height and pad thickness.

[0037] In order to achieve the above object, the technical solution adopted by the present invention is:

[0038] A method for simplifying the determination of maximum stress and maximum energy absorption per unit volume of a material buffer curve comprises the following steps:

[0039] Step 1. Meet the requirements of the relevant standard GB / T8167-2008. Consider the production dimensions and specifications of the cushioning material sample, as well as the sample size, drop weight, and drop height range required by the impact testing machine. When the sample cross-sectional area A along the impact direction and the cushion thickness t are maximized, and the drop height h and drop weight m are minimized, the static stress σs takes the minimum value (σs)Min, h / t takes the minimum value (h / t)Min, and em takes the theoretical minimum value (em)Min. Conversely, σs takes the maximum value (σs)Max, h / t takes the maximum value (h / t)Max, and em takes the theoretical maximum value (em)Max. The minimum value (em)Min of em should be slightly larger than the theoretical minimum value. The determination of (em)Max should also be based on the energy absorption curve of the static compression of the cushioning pad. Samples were prepared in accordance with the provisions of the standard GB / T8168-2008, and pre-treated in a constant temperature and humidity chamber in accordance with the standard GB / T4857.2-2005. A quasi-static compression test was then performed on the sample using a universal material testing machine in accordance with the standard GB / T8168-2008 until the sample was densified. The pressure and displacement data of the buffer material were measured, and both were standardized using the bearing area A of the buffer material and the sample thickness t, respectively. Finally, the static compression σ(ε)-ε curve of the buffer material was obtained, and the corresponding unit volume energy absorption and strain E(ε)-ε curve was obtained by integrating the curve. Densification strain ε of the buffer material D =1-1.4ρ / ρ s =1-1.4ρ * ,ρ * is the relative density of the cushioning material, ρ and ρs are the densities of the cushioning material and its base material respectively. The energy absorption per unit volume of the cushioning material corresponding to εD is called the densified energy absorption per unit volume ED. Taking the dynamic coefficient c0 = 1.5, then (e m ) Max =c0E D , and finally em∈[(em)Min,(em)Max].

[0040] Step 2: Increase both σs and h / t simultaneously, or fix one while increasing the other continuously, or alternate between them, or randomly select one, as long as the product of the two (maximum energy absorption per unit volume) increases from (em)Min to (em)Max. Assume that the em value is divided into nc points (em)i with a certain spacing, and the corresponding σs and h / t values ​​are (σs)i and (h / t)i, respectively. The serial variable i = 1, 2, 3, ... nc, and generally nc = 10 to 20.

[0041] Step 3. Corresponding to any (em)i value in step (2), while ensuring that the corresponding (σs)i and (h / t)i values ​​remain unchanged, refer to the relevant standard GB / T8167-2008 and the production size specifications of the cushioning material samples and the drop height range of the impact testing machine, and take five groups of different drop height h and pad thickness t value combinations, namely (h)j and (t)j, where j is another serial variable, j=1, 2, 3, 4, 5; at the same time, select the cross-sectional length Lj and width Wj of the cushioning pad along the impact direction, as well as the mass (m)j of the drop hammer, to ensure that (σs)i=(m)jg / (Lj×Wj). For each group of (m)j, (h)j, (t)j, Lj, and Wj combined values, the corresponding samples were pre-treated in a constant temperature and humidity chamber according to the provisions of standard GB / T4857.2-2005, and then the cushioning material padding samples were subjected to a drop impact test according to standard GB / T8167-2008 to obtain the corresponding [G] measurement value ([G])j). For the same type of cushioning material, there is a definite C-em function relationship; under fixed (em)i and (h / t)i values, there is naturally a definite σm. The ([G])j values ​​of the five groups should be close to equal, and their average value is taken as the [G] value ([G])i corresponding to (em)i, that is, Finally, the corresponding dynamic buffer coefficient (C) of this group is calculated i =((G) i +1) / (h / t) i .

[0042] Step 4: For each maximum unit volume energy absorption (em)i value in step (2), repeat step (3) to obtain all nc type value points ((em)i, (C)i) of the dynamic cushioning coefficient and maximum unit volume energy absorption relationship curve, i = 1, 2, 3...nc.

[0043] Step 5. For most cushioning materials, the cushioning effect is generated by the deformation of enclosed gas, such as foam, corrugated cardboard, honeycomb cardboard, bubble cushion and air pillow. Based on the ideal gas model, when the units of the two are consistent, the maximum stress and the maximum energy absorption per unit volume numerically satisfy the following relationship: a and b are dimensionless relationship coefficients, e = 2.71828. Combining with formula (10), we get Based on this formula, nc ((em)i, (C)i) coordinate points are fitted to obtain the specific values ​​of the relationship coefficients a and b.

[0044] Step 6. Refer to the production size specifications of the buffer material sample mentioned in step (1), as well as the sample size and drop weight range required by the impact tester, and take a reasonable value range of static stress σs [((σs)Min, (σs)Max]. Define another serial variable k, and take a series of σs values ​​(σs)k from (σs)Min to (σs)Max, ensuring that (σs)k increases with the increase of k value, k = 1, 2, 3...ns. From k = 1 to ns, at any ratio of drop height to pad thickness h / t, calculate the maximum unit volume energy absorption (e) corresponding to the static stress (σs)k on the [G]-σs buffer curve to be constructed according to the above formula (13). m ) k =(σ s ) k h / t. Then, according to the relationship between the dynamic coefficient of the buffer material obtained in step (5) and the maximum unit volume energy absorption, the dynamic buffer coefficient corresponding to (em)k is directly calculated. Finally, according to the above formula (11), the corresponding [G] value ([G]) is calculated k =(C) j Based on the calculated coordinate points ((σs)k, ([G])k), these coordinate points are connected by means of appropriate curve interpolation or fitting to obtain the [G]-σs buffer curve to be constructed.

[0045] The beneficial effects of the present invention are:

[0046] (1) It is only necessary to conduct a limited number of impact tests on the buffer material, and then generate a relationship between the maximum stress and the maximum energy absorption per unit volume of the buffer material. From this, the [G]-σs buffer curve of the buffer material under any combination of drop height and pad thickness can be constructed, thereby achieving the continuity of the buffer curve with respect to drop height and pad thickness.

[0047] (2) There is no need to conduct tests on a variety of drop weights at different drop heights and pad thickness combinations as in the existing method. In order to first test the relationship curve between the maximum stress and the maximum unit volume energy absorption of the buffer material, only 50 to 100 test samples are needed, and the corresponding sample purchase and production costs are low.

[0048] (3) This method requires at most a limited number of impact tests. Compared with the existing [G]-σs buffer curve determination method, the number of impact tests in this method is significantly reduced, and the testing process becomes simpler.

[0049] (4) Compared with the existing [G]-σs buffer curve determination method, the number of samples required is greatly reduced, and the total time consumption such as sample preparation and test interval waiting is greatly reduced.

[0050] (5) The number of samples and the number of impact tests required are greatly reduced, and the total cost of using the corresponding test equipment is also greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a schematic diagram of the principle of dynamic impact test of cushioning pad;

[0052] Figure 2 This is a diagram of the DY-2 impact testing machine;

[0053] Figure 3 It is the static stress-strain σ(ε)-ε curve of closed-cell EVA foam material (ρ = 106 kg / m3);

[0054] Figure 4 It is the static unit volume energy absorption-strain E(ε)-ε curve of closed-cell EVA foam material (ρ=106kg / m3);

[0055] Figure 5 This is the dynamic cushioning coefficient-maximum unit volume energy absorption C-em curve of closed-cell EVA foam material (ρ=106kg / m3);

[0056] Figure 6 It is the [G]-σs cushioning curve of closed-cell EVA foam material (ρ=106kg / m3) at h / t=9. DETAILED DESCRIPTION

[0057] The present invention is further described below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0058] like Figure 1 As shown in the figure, the relationship between the maximum stress of the buffer material and the maximum energy absorption per unit volume is constructed to simplify its [G]-σ s The measurement process of the cushioning curve can be used to construct the [G]-σ under any combination of drop height h and pad thickness t of the cushioning material. s Buffer curve.

[0059] A method for simplifying the determination of maximum stress and maximum energy absorption per unit volume of a material buffer curve comprises the following steps:

[0060] Step 1: Determine the maximum energy absorption per unit volume e m The minimum value e mMin and the maximum value e mMax .

[0061] In accordance with the requirements of the relevant standard GB / T8167-2008, considering the production size of the buffer material sample, the sample size required by the impact tester, the drop weight and the drop height range, according to formula (1), when the cross-sectional area A of the sample along the impact direction is the largest and the drop weight m is the smallest, the static stress σ s Take the minimum value, otherwise σ s Take the maximum value. When the static stress σ s When the drop height h takes the minimum value and the pad thickness t takes the maximum value, e m Take the theoretical minimum value e mMin ; When σ s When and h take the maximum value and t takes the minimum value, e m Take the theoretical maximum value e mMax .

[0062] This is only a theoretical prediction. m The minimum value of can be slightly larger than the theoretical minimum value; similarly, under actual experimental conditions, the maximum drop weight is rarely used to impact a cushioning pad with a small cross-sectional area and a thin thickness. In this case, the pad deformation will be in a densified state, and the drop weight acceleration value will be very high, which will cause damage to the acceleration sensor. Therefore, e mMax The determination must also be combined with the energy absorption curve of the static compression of the buffer pad. Samples are made in accordance with the provisions of standard GB / T8168-2008, and the samples are pre-treated using a constant temperature and humidity chamber in accordance with the provisions of standard GB / T4857.2-2005. Then, in accordance with the provisions of standard GB / T8168-2008, a quasi-static compression test is performed on the sample with the help of a universal material testing machine until the sample is densified, and the pressure and displacement data of the buffer material are directly measured. Both are standardized using the bearing area A of the buffer material and the sample thickness t, and finally the static compression σ(ε)-ε curve of the buffer material is obtained. The corresponding unit volume energy absorption and strain E(ε)-ε curve is obtained by integrating the curve.

[0063] Here we define a physical term - the densification strain ε of the buffer material D , refers to the strain when the entire buffer material is compressed and the corresponding stress begins to increase sharply. Generally speaking, the densification strain of the buffer material under dynamic impact is slightly greater than the densification strain of its static compression ε D The calculation formula of the static densification strain of the buffer material is (Gibson LJ, Ashby M F. Cellular Solids: Structure and Properties (2nd ed). Cambridge, UK: Cambridge University Press, 1997)

[0064] εD =1-1.4ρ / ρ s =1-1.4ρ * (18)

[0065] Where, ρ * is the relative density of the cushioning material, ρ and ρ s are the densities of the cushioning material and its base material, respectively. Static densification strain ε D The corresponding energy absorption per unit volume of the cushioning material is called the densified energy absorption per unit volume E D Taking into account the influence of dynamic effects, or the situation where the impact slightly exceeds the densification strain and causes a sharp increase in dynamic stress, the dynamic coefficient c0 is generally taken as around 1.5. Then e mMax The value of e can be determined according to the following formula mMax =c0E D (19)

[0066] So far, e has been determined m The minimum and maximum values ​​of e m ∈[e mMin ,e mMax ].

[0067] Step 2: The maximum energy per unit volume is absorbed m Divide into several value points e with approximately uniform spacing mi .

[0068] The maximum energy absorption per unit volume is reduced from e mMin to e mMax , divided into n e approximately evenly spaced value points e mi , generally n e =10~20, then i=1,2,3...n e Here n e is an integer representing the value point e mi , and i is an ordinal variable.

[0069] Step 3: Measure and obtain the maximum energy absorption value per unit volume e mi The corresponding maximum stress value σ mi .

[0070] For each maximum unit volume energy absorption value e in step (2) mi , refer to the requirements of the relevant standard GB / T8167-2008 and the production size of the buffer material sample, as well as the sample size and drop height range of the impact tester, and take five different groups of static stress (σ s ) j , Drop height (h) j and pad thickness (t)j The combination value (j is another serial variable, j = 1, 2, 3, 4, 5) all satisfies the maximum unit volume energy absorption (σ s ) j (h) j / (t) j =e mi For each group of σ s Value (σ s ) j , and then refer to the configuration of the impact tester drop weight weight, give the corresponding reasonable drop weight mass (m) j , and then calculate the cross-sectional area A of the pad along the impact direction according to formula (1) j =(m) j g / (σ s ) j and the corresponding cross-sectional length L j and width W j , it is necessary to ensure that the pad size meets the standard GB / T8167-2008, the production size of the cushioning material sample and the sample size requirements of the impact testing machine.

[0071] For each group (m) j 、(h) j 、(t) j 、A j , L j and W j The sample was pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T4857.2-2005, and then the sample was pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T8167-2008. Figure 2 The DY-2 impact tester shown in the figure is used to perform a drop impact test on the cushioning material pad sample, and the corresponding [G] measurement value ([G]) is obtained. j ; According to formula (15), the maximum stress (σ m ) j =(σ s ) j (([G]) j +1). According to the above theory, for the same type of cushioning material, the maximum stress of the five groups should be close to the same, and their average value is taken as the corresponding e mi The maximum stress value

[0072] Step 4: Measure n e The maximum stress and maximum energy absorption per unit volume (e mi ,σ mi ).

[0073] For each maximum unit volume energy absorption value e in step (2) mi , repeat step (3) to get all n e The maximum energy absorption per unit volume and the maximum stress value point (e mi ,σ mi ), i=1,2,3...n e .

[0074] Step 5: Construct the maximum stress σ m and the maximum energy absorption per unit volume e m relationship curve.

[0075] With the help of a certain relationship equation, we can fit the n obtained in step (4) e Individual value points (e mi ,σ mi ) to obtain the specific relationship between maximum stress and maximum energy absorption per unit volume. For most cushioning materials, such as foam, corrugated cardboard, honeycomb cardboard, bubble cushions, and air pillows, which rely on the deformation of enclosed gases to produce their cushioning effect, based on the ideal gas model, when the units of the two are consistent, the maximum stress and maximum energy absorption per unit volume numerically satisfy the following relationship (Daum MA simplified process for determining cushion curves the stress-energy method. http: / / talkpkg.com / Papers-Presentations / Presentation / Daum%20Matthew%20Dimensions06%20paper.pdf.1999):

[0076] Where a and b are dimensionless coefficients, whose values ​​depend on the material and density of the buffer material; e is a natural constant, e = 2.71828. This invention only supports buffer materials whose maximum stress and maximum unit volume energy absorption satisfy this relationship. For other types of buffer materials, according to their buffering mechanism, other relationship formulas can be used to fit the maximum stress and maximum unit volume energy absorption. e (e mi ,σ mi ) point, and the values ​​of the relationship coefficients a and b in formula (20) are obtained by curve fitting.

[0077] Step 6: Use the relationship between maximum stress and maximum energy absorption per unit volume to construct [G]-σ for any combination of drop height h and pad thickness t of the cushioning material. s Buffer curve.

[0078] Refer to the production size limit of the buffer material sample mentioned in step (1), as well as the sample size and drop weight range required by the impact tester. Of course, you can also take any static stress σ s A range of values, assuming σ s The minimum and maximum values ​​of (σ s ) Min and (σ s ) Max . Define another serial variable k, in the interval [((σ s ) Min ,(σ s ) Max ] from (σ s ) Min to (σ s ) Max Take any series of σ s Value (σ s ) k , to ensure (σ s ) k As the value of k increases, it is generally increased by the interval [(σ s ) Min ,(σ s ) Max ] is divided equally into n s -1 equal parts and get this n s σ s value.

[0079] From k=1 to n s , under the combination of drop height h and pad thickness t, calculate the [G]-σ to be constructed according to the above formula (16) s Static stress on the buffer curve (σ s ) k The corresponding maximum energy absorption per unit volume (e m ) k =(σ s ) k h / t. Then, according to the relationship between the maximum stress and the maximum energy absorption per unit volume obtained in step (5), we can directly calculate (e m ) k The corresponding maximum stress (σ m ) k Finally, according to the above formula (15), the corresponding [G] value ([G]) is calculated. k =(σ m ) k / (σ s ) k -1.

[0080] Based on the calculated coordinate point ((σ s )k ,([G]) k ), by connecting these coordinate points with the help of appropriate curve interpolation or fitting, we can get the [G]-σ to be constructed s Buffer curve. n s The larger the value, the more and denser the coordinate points on the constructed buffer curve will be. Finally, these coordinate points will be directly connected to draw the final constructed [G]-σ s Buffer curve.

[0081] Theoretical basis for the feasibility of the inventive method:

[0082] As mentioned above, the cushioning material resists the stress during impact. With ε and It is related that when the impact velocity v is at a low level (v < 15m / s), the strain rate effect of the dynamic stress-strain curves of honeycomb, corrugated and open-cell foam materials can be ignored; a large number of studies attempting to construct the strain rate effect of closed-cell foams also show that the key factor in the dynamic stress-strain curve is ε, not The strain rate effect is relatively small. During the drop hammer impact, the strain rate can also be expressed as

[0083]

[0084] At the beginning of the impact, the speed of the hammer is the largest, and the strain rate of the buffer material is the largest. Combined with formula (5), the initial strain rate of the buffer material can be obtained: for

[0085]

[0086] From this formula, we can see that only a very high drop height will cause a large strain rate. According to the standards GB / T4857.5-1992, GB / T 4857.17-2017 and GB / T 4857.18-1992, the maximum drop height strength of the product is only 2.1m. Therefore, under normal product circulation conditions, the strain rate effect of the foam material response caused by the impact speed of the package drop is usually very small and can be ignored. With ε and The relationship can be simplified to

[0087] σ≈f2(ε) (14);

[0088] The maximum stress σ m Assuming it as a variable, we can get from formula (8)

[0089] σ m =σ s ([G]+1)=f1(ε m) (15);

[0090] Also the maximum unit volume energy absorption e m As a variable, formula (6) can be obtained

[0091]

[0092] It can be seen from this that σ m =σ s ([G]+1) and e m =σ s h / t are both ε m From the above two equations, it can be seen that for a certain buffer material, there must be a certain functional relationship that converts the σ of each impact between the two s h / t and σ s The ([G]+1) values ​​are linked to each other, i.e.

[0093] σ s ([G]+1)=f3(σ s h / t) (17).

[0094] Example:

[0095] Taking a closed-cell EVA (Ethylene Vinyl Acetate) foam material as an example, more than ten drop hammer impact tests were conducted to establish the relationship between its maximum stress and maximum energy absorption per unit volume. This was used to construct the [G]-σ of this cushioning material under any combination of drop height h and pad thickness t. s Buffer curve, and combined with the [G]-σ measured by the corresponding test of the constructed curve s The cushioning curve is used to illustrate the feasibility and beneficial effects of this method. The density of the closed-cell EVA foam is ρ = 80 kg / m 3 The constructed curve corresponds to any drop height h = 500mm and pad thickness t = 40mm. The specific implementation steps of this case are as follows:

[0096] (1) According to the relevant standard GB / T8167-2008, the length and width of the cross section of the pad sample along the impact direction shall not be less than 100mm×100mm, and the pad thickness t shall not be less than 25mm. The closed-cell EVA foam used (ρ=80kg / m 3 ) thickness specifications are 35, 40, 50 and 60 mm. All impact tests are performed using Figure 2 The DY-2 impact tester shown in the figure has a drop weight range of m = 2 to 50 kg, a maximum drop height of 1200 mm, and a maximum impact size of the test bench sample of 210 mm × 210 mm. For ease of operation, the drop height of the impact tester should not be less than 40 mm. According to formula (1), the static stress σs The minimum value of is 2×9.8 / (0.21×0.21)=0.444kPa, static stress σ s The maximum value of is 50×9.8 / (0.1×0.1)=49kPa. In summary, σ s =0.444~49kPa, h=40~1200mm, t=35~60mm. Of course, thicker gasket samples can be obtained by stacking as needed. Finally, e m The theoretical minimum value e mMin =0.444×40 / 60kPa=0.296kPa and the theoretical maximum value e mMax =49×1200 / 35kPa=1680kPa.

[0097] e m The minimum value e mMin Take a value slightly larger than the theoretical minimum, such as e mMin =1kPa. According to the provisions of standard GB / T8168-2008, the sample is made. The sample thickness can be t=40mm. The sample is pre-treated in a constant temperature and humidity chamber according to the provisions of standard GB / T 4857.2-2005. Then, according to the provisions of standard GB / T 8168-2008, a static compression test is performed on the sample with the help of a universal material testing machine until the sample is densified. The pressure and displacement data of the buffer material are directly measured. The two are standardized by the bearing area of ​​the buffer material and the sample thickness respectively. Finally, the static compression σ(ε)-ε curve of the buffer material is obtained, as shown in Figure 3 As shown. Then the corresponding unit volume energy absorption and strain E(ε)-ε curve is obtained by integrating the curve, as shown Figure 4 shown.

[0098] The density of the closed-cell EVA foam material is ρ=80 kg / m 3 and the density of the solid substrate ρ s =950kg / m 3 , so according to the above formula (18), the densification strain ε of the buffer material can be calculated D =1-1.4ρ / ρ s =1-1.4×80 / 950=0.8821, the corresponding strain should be Figure 4 The corresponding energy absorption per unit volume of densification can be obtained from the E(ε)-ε curve D =235.4341kPa, and finally according to the above formula (19) we can calculate e mMax =c0×E D =1.5×235.4341kPa=353.1512kPa. Finally, e was determined. mThe minimum and maximum values ​​of e m ∈[1,353.1512].

[0099] (2) Change the maximum unit volume energy absorption from e mMin =1kPa to e mMax =353.1512kPa, divided into n e = 10 approximately evenly spaced value points e mi . From i=1,2,3...n e , e mi The values ​​are 1.0000kPa, 40.1279kPa, 79.2558kPa, 118.3837kPa, 157.5116kPa, 196.6396kPa, 235.7675kPa, 274.8954kPa, 314.0233kPa and 353.1512kPa respectively.

[0100] (3) For each maximum unit volume energy absorption value e in step (2) mi , refer to the requirements of the relevant standard GB / T8167-2008, as well as the production size of the buffer material sample mentioned in step (1), the sample size of the impact tester and the drop height range, and take five different groups of static stress (σ s ) j , Drop height (h) j and pad thickness (t) j The combination value (j is another serial variable, j = 1, 2, 3, 4, 5) all satisfies the maximum unit volume energy absorption (σ s ) j (h) j / (t) j =e mi For each group of σ s Value (σ s ) j , and then refer to the configuration of the impact test machine drop weight mass, give the corresponding reasonable drop weight (m) j , and then calculate the cross-sectional area A of the pad along the impact direction according to formula (1) j =(m) j g / (σ s ) j , and give the corresponding cross-sectional length L j and width W j , make sure that the pad size meets the requirements of GB / T 8167-2008, the production size of the cushioning material sample and the sample size of the impact testing machine. m1 =1kPa, (σ s )j 、(h) j 、(t) j 、(m) j 、A j , L j and W j There are five possible combinations of values ​​listed in Table 1.

[0101] Table 1 corresponds to e m1 =1kPa(σ s ) j 、(h) j 、(t) j 、(m) j 、A j , L j and W j Five combination values

[0102]

[0103] For each group (m) j 、(h) j 、(t) j 、A j , L j and W j The samples were pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T4857.2-2005, and then the samples were treated in a constant temperature and humidity chamber according to the provisions of GB / T 8167-2008. Figure 2 The DY-2 impact tester shown in the figure is used to perform a drop impact test on the cushioning material pad sample, and the corresponding [G] measurement value ([G]) is obtained. j ; According to formula (15), the maximum stress (σ m ) j =(σ s ) j (([G]) j +1), the maximum stress of the five groups of buffer materials is averaged to obtain the corresponding e mi The maximum stress σ mi For example, corresponding to e m1 =1kPa,σ m1 The average value is 31.1313kPa.

[0104] (4) For each maximum unit volume energy absorption value e in step (2) mi , repeat step (3) to get all n e = 10 points of maximum energy absorption per unit volume and maximum stress value (e mi ,σ mi ). From i=1,2,3...n e,σ mi The values ​​are 31.1313kPa, 50.0853kPa, 78.1232kPa, 120.7065kPa, 178.4567kPa, 290.2779kPa, 437.8609kPa, 699.3343kPa, 1071.9693kPa and 1694.7897kPa respectively.

[0105] (5) For the closed-cell EVA foam material, the n obtained in step (4) is fitted based on the aforementioned formula (20). e = 10 type value points (e mi ,σ mi ), construct the maximum stress σ of the buffer material m and the maximum energy absorption per unit volume e m The relationship curve, such as Figure 5 As shown, a=30.20399 and b=0.0114 are obtained.

[0106] Then the maximum stress σ of the EVA foam material is obtained m and the maximum energy absorption per unit volume e m The relationship between Where e is a natural constant, e=2.71828.

[0107] (6) As described in step (1), according to the relevant standard GB / T 8167-2008, the length and width of the cross section of the gasket sample along the impact direction shall not be less than 100mm×100mm, and the maximum impact size of the test bench sample shall be 210mm×210mm; the mass range of the drop hammer of the DY-2 impact testing machine used is m=2~50kg. Then according to formula (1), the static stress σ s The minimum value of is 2×9.8 / (0.21×0.21)=0.444kPa, static stress σ s The maximum value is 50×9.8 / (0.1×0.1)=49kPa. s The range of values ​​of σ is given s A value range of which the minimum and maximum values ​​are (σ s ) Min =1kPa and (σ s ) Max =20kPa. Take the integer variable n s =100, the interval [(σ s ) min ,(σ s ) max ] is divided equally into n s -1 equal parts, ensure that the sequence variable k = 1 to n s When increasing (σ s) k Increase in sequence.

[0108] The [G]-σ of the buffer material to be constructed in this case s The buffer curve corresponds to a drop height of h = 500 mm and a pad thickness of t = 40 mm. Of course, [G]-σ can also be constructed for other drop heights and pad thickness combinations. s Buffer curve. According to the above formula (16), calculate the [G]-σ to be constructed s Static stress on the buffer curve (σ s ) k The corresponding maximum energy absorption per unit volume (e m ) k =(σ s ) k h / t. Then, according to the relationship between the maximum stress and the maximum energy absorption per unit volume obtained in step (5), we can directly calculate (e m ) k The corresponding maximum stress Finally, according to the above formula (15), the corresponding [G] value ([G]) is calculated k =(σ m ) k / (σ s ) k -1.

[0109] Based on the calculated coordinate point ((σ s ) k ,([G]) k ), by means of appropriate curve interpolation or fitting, these coordinate points are connected to obtain the [G]-σ of the EVA foam cushioning material to be constructed. s Buffer curve. If n s The larger the value, the more and denser the coordinate points on the constructed buffer curve will be. By directly connecting these coordinate points one after another, the final [G]-σ can be constructed. s Cushioning curve. [G]-σ of the EVA foam cushioning material constructed in this case under the combination of drop height h = 500mm and pad thickness t = 40mm s Buffer curve, such as Figure 6 shown.

[0110] At the same time, the static stresses were taken as 2kPa, 4kPa, 6kPa, 8kPa, 10kPa, 12kPa, 14kPa, 16kPa, 18kPa and 18kPa respectively. According to GB / T8167-2008 "Test method for dynamic compression of cushioning materials for packaging", the test specimens with a thickness of 40mm of the closed-cell EVA foam material were prepared, and the length and width of the cross section in the impact direction were both in the range of 100mm to 210mm; according to GB / T4857.2-2005 "Basic tests for packaging and transport packages - Part 2 - Temperature and humidity adjustment treatment", the specimens were pretreated in a constant temperature and humidity chamber; and then according to GB / T8167-2008 "Test method for dynamic compression of cushioning materials for packaging", the specimens were pretreated in a constant temperature and humidity chamber. Figure 2 The DY-2 impact testing machine produced by Xi'an Guangbo Testing Equipment Co., Ltd. was used to perform impact tests on the samples. The [G] values ​​obtained were 19.3078, 12.5512, 10.6002, 10.4726, 11.5367, 13.3569, 15.1187, 17.9929, 20.9028 and 25.7321 respectively. These test values ​​are plotted on Figure 6 , it can be seen that the two are very consistent, proving the reliability of this buffer curve construction method.

[0111] From this embodiment, the present invention first constructs the relationship between the maximum stress and the maximum unit volume energy absorption of the buffer material to construct the [G]-σ of the buffer material under any combination of drop height and pad thickness. s Buffer curve, the beneficial effect of this method is obvious.

Claims

1. A simplified method for determining the maximum stress and maximum energy absorption per unit volume of a material buffer curve, characterized in that: The following steps are involved: Step 1: Determine the maximum energy absorption per unit volume e m The minimum value e mMin and the maximum value e mMax : Step 2: The maximum energy per unit volume is absorbed m Divide into several value points e with approximately uniform spacing mi ; Step 3: Measure and obtain the maximum energy absorption value per unit volume e mi The corresponding maximum stress value σ mi ; Step 4: Measure n e The maximum stress and maximum energy absorption per unit volume (e mi ,σ mi ); Step 5: Construct the maximum stress σ m and the maximum energy absorption per unit volume e m The relationship curve of Step 6: Use the relationship between maximum stress and maximum energy absorption per unit volume to construct [G]-σ for any combination of drop height h and pad thickness t of the cushioning material. s Buffer curve.

2. The maximum stress and maximum energy per unit volume method for simplified measurement of a material buffer curve according to claim 1, characterized in that: Determine the maximum energy absorption per unit volume e as described in step 1 m The minimum value e mMin and the maximum value e mMax : Meet the requirements of the relevant standard GB / T8167-2008, taking into account the production size of the buffer material sample, the sample size required by the impact tester, the drop weight and the drop height range, according to the formula σ s = mg / A (1) When the cross-sectional area A of the sample along the impact direction is the largest and the mass m of the falling hammer is the smallest, the static stress σ s Take the minimum value, otherwise σ s Take the maximum value when the static stress σ s When the drop height h takes the minimum value and the pad thickness t takes the maximum value, e m Take the theoretical minimum value e mMin ; When σ s When and h take the maximum value and t takes the minimum value, e m Take the theoretical maximum value e mMax ; e mMax The determination must also be combined with the energy absorption curve of the static compression of the buffer pad; samples are made in accordance with the provisions of standard GB / T8168-2008, and the samples are pre-treated using a constant temperature and humidity chamber in accordance with the provisions of standard GB / T4857.2-2005. Then, in accordance with the provisions of standard GB / T8168-2008, a quasi-static compression test is performed on the sample with the help of a universal material testing machine until the sample is densified, and the pressure and displacement data of the buffer material are directly measured. Both are standardized using the bearing area A of the buffer material and the sample thickness t, and finally the static compression σ(ε)-ε curve of the buffer material is obtained. The corresponding unit volume energy absorption and strain E(ε)-ε curve is obtained by integrating the curve; The calculation formula for the static densification strain of the buffer material is ε D =1-1.4ρ / ρ s =1-1.4ρ * (18), where ρ * is the relative density of the cushioning material, ρ and ρ s are the density of the buffer material and its base material, the static densification strain ε D The corresponding energy absorption per unit volume of the cushioning material is called the densified energy absorption per unit volume E D , take the dynamic coefficient c0 = 1.5, e mMax The value of e can be determined according to the following formula mMax =c0E D (19), determined e m The minimum and maximum values ​​of e m ∈[e mMin ,e mMax ].

3. The maximum stress and maximum energy absorption per unit volume method for simplified measurement of a material buffer curve according to claim 1, characterized in that: The maximum unit volume energy absorption e in step 2 m Divide into several value points e with approximately uniform spacing mi :The maximum energy per unit volume is absorbed from e mMin to e mMax , divided into n e approximately evenly spaced value points e mi , generally n e =10~20, then i=1,2,3...n e Here n e is an integer representing the value point e mi , and i is an ordinal variable.

4. The maximum stress and maximum energy absorption per unit volume method for simplified measurement of a material buffer curve according to claim 1, characterized in that: The measurement described in step 3 obtains each maximum unit volume energy absorption value e mi The corresponding maximum stress value σ mi , for each maximum unit volume energy absorption value e in step 2 mi , refer to the requirements of the relevant standard GB / T8167-2008 and the production size of the buffer material sample, as well as the sample size and drop height range of the impact tester, and take five different groups of static stress (σ s ) j , Drop height (h) j and pad thickness (t) j The combination value (j is another serial number variable, j = 1, 2, 3, 4, 5) all satisfies the formula The calculated maximum energy absorption per unit volume (σ s ) j (h) j / (t) j =e mi ; For each group of σ s Value (σ s ) j , and then refer to the configuration of the impact tester drop weight weight, give the corresponding reasonable drop weight mass (m) j , and then according to the formula σ s = mg / A (1) Calculate the cross-sectional area A of the pad along the impact direction j =(m) j g / (σ s ) j and the corresponding cross-sectional length L j and width W j ; For each group (m) j 、(h) j 、(t) j 、A j , L j and W j The sample was pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T4857.2-2005, and then the cushioning material liner sample was subjected to a drop impact test using a DY-2 impact testing machine according to the provisions of GB / T8167-2008 to obtain the corresponding [G] measurement value ([G]) j According to the formula σ m =σ s ([G]+1)=f1(ε m The maximum stress of this group (σ m ) j =(σ s ) j (([G]) j +1), according to the above theory, for the same type of buffer material, the maximum stress of the five groups should be close to the same, and their average value is taken as the corresponding e mi The maximum stress value 5. The maximum stress and maximum energy absorption per unit volume method for simplified determination of a material buffer curve according to claim 1, characterized in that: Measure n in sequence as described in step 4 e The maximum stress and maximum energy absorption per unit volume (e mi ,σ mi ), for each maximum unit volume energy absorption value e in step 2 mi , repeat step 3 to get all n e The maximum energy absorption per unit volume and the maximum stress value point (e mi ,σ mi ), i=1,2,3...n e .

6. The maximum stress and maximum unit volume energy absorption method for simplified measurement of a material buffer curve according to claim 1, characterized in that: Construct the maximum stress σ as described in step 5 m and the maximum energy absorption per unit volume e m The relationship curve is fitted with the n obtained from step 1 to step 4 by means of a certain relationship equation. e Individual value points (e mi ,σ mi ), the specific relationship between the maximum stress and the maximum energy absorption per unit volume is obtained. For cushioning materials that rely on the deformation of enclosed gas to produce a cushioning effect, the maximum stress and the maximum energy absorption per unit volume numerically satisfy the following relationship: Where a and b are dimensionless coefficients, whose values ​​depend on the material and density of the cushioning material; e is a natural constant, e = 2.7182, according to n e (e mi ,σ mi ) point, and the values ​​of the relationship coefficients a and b in formula (20) are obtained by curve fitting.

7. The maximum stress and maximum energy absorption per unit volume method for simplified measurement of a material buffer curve according to claim 1, characterized in that: The relationship between maximum stress and maximum energy absorption per unit volume described in step 6 is used to construct the [G]-σ for any combination of drop height h and pad thickness t of the cushioning material. s Buffer curve: Refer to the production size limit of the buffer material sample mentioned in step 1, as well as the sample size and drop weight range required by the impact tester. Of course, you can also take any static stress σ s A range of values, assuming σ s The minimum and maximum values ​​of (σ s ) Min and (σ s ) Max . Define another serial variable k, in the interval [((σ s ) Min ,(σ s ) Max ] from (σ s ) Min to (σ s ) Max Take any series of σ s Value (σ s ) k , to ensure (σ s ) k As the value of k increases, it is generally increased by the interval [(σ s ) Min ,(σ s ) Max ] is divided equally into n s -1 equal parts and get this n s σ s value.; From k=1 to n s , under the combination of drop height h and pad thickness t, according to the above formula Calculate the required construction [G]-σ s Static stress on the buffer curve (σ s ) k The corresponding maximum energy absorption per unit volume (e m ) k =(σ s ) k h / t, and then according to the relationship between the maximum stress and the maximum unit volume energy absorption obtained in step (5), directly calculate (e m ) k The corresponding maximum stress (σ m ) k Finally, according to the formula σ m =σ s ([G]+1)=f1(ε m )(15), calculate the corresponding [G] value ([G]) k =(σ m ) k / (σ s ) k -1, based on the calculated coordinate point ((σ s ) k ,([G]) k ), by connecting these coordinate points with the help of appropriate curve interpolation or fitting, we can get the [G]-σ to be constructed s Buffer curve. n s The larger the value, the more and denser the coordinate points on the constructed buffer curve will be. Finally, these coordinate points will be directly connected to draw the final constructed [G]-σ s Buffer curve.

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