In industrial and agricultural production and daily life, there are many cases of cover cracking due to thermal expansion and contraction. It directly affects the circulation and use of commodities, causing liquid leakage and even causing fire accidents. In elastic mechanics, the deformation is proportional to the stress. Hangzhou University of Electronic Science and Technology adopted the method of deformation analysis to solve the problem of calculation of the internal stress distribution and fracture strength of the rope. After improving the derivation method and the extension concept, new structural functions were obtained.
1 Characteristic and strain analysis of cover
The geometry of the cover can be regarded as a combination of a disc and a ring. For a disk with radius and. If the radial and chord shrinkage ratios of the disk are the same, the relative radial shrinkage ratio PD = △ R ／ (2R) = △ R ／ R, and the relative shrinkage ratio of the circumference PC = 2π △ R ／ (2πR) = △ R / R, the comparison between the two PC = PD = △ R / R, that is, there is no obvious advantage in the relative shrinkage ratio of the radial direction to the chord direction.
2 Stress analysis
2.1 Effect of deformation on stress
According to the stress is proportional to the relative elongation, the shrinkage stress of the isotropic material in the warp, weft and direction is equivalent, and the direction of the tear of the cover should be irregular. According to the tensile strength of the polymer material and the actual radial force converging on the center of the circle, even if the stress exceeds the strength of the material and it breaks, it should occur near the center of the circle where the stress is concentrated. The above 2 points are consistent with the fact that the split occurred at the edge of the cover ring.
2.2 The influence of polymer material molding process on mechanical properties
Considering that there are many LDPE branches, the crystallinity is about 55% to 60%; HDPE is linear, with few branches, and the crystallinity is 85% to 90%. When injection molding from the center of the disc, due to fluidity, The linear shape of the polymer material in the disc part of the cover is mainly arranged in a radial direction due to radial flow. After cooling and forming, the plastic cover has a high radial tensile strength, and the chord tensile strength will be significantly lower than the radial direction. Under the shrinkage rate, it is easy to crack radially. The crystalline orientation of polymer materials has a significant effect on strength, which can be understood from the mechanical properties of biaxially oriented polypropylene film BOPP. For example: according to the 1: 1 PVC packing belt with filler, the difference in warp and weft strength after stretching and setting is significant. The mechanical strength and even air permeability of plastics are related to whether there are fillers, filler shapes and linear macromolecules whether they are crystallized, etc. After the stretched orientation of the shaped polymer, its tensile strength is greatly improved and the weft direction is easy to tear Split (typically as a strap). The author has conducted a large number of impact tests on the injection molded polystyrene (PS), transparent discs and lid-like PS trays at the center gate. Statistics show that the impact cracks are generally carried out in the radial direction; local sample bending tests show that The radial bending performance of PS is much higher than the chord direction. Under the action of chord bending moment, the fan-shaped PS sample or PS thin disc is easily broken along the radial flow line.
3 The effect of radial yielding of cover ring structure on stress
The actual cover working mechanism is the inner part and the cover, and the interaction between the two is external force. For the convenience of analysis, it is assumed that the contents do not shrink with temperature, and the diameter is the same as the cover.
3.1 The influence of concession on the radial and chord stress performance
When the disc part of the cover shrinks radially, due to the flexibility of the polymer material, the connection angle between the cover ring and the disc part will produce a certain amount of creep, which gives the cover ring part a certain ability to reform (reform ability) ), The result of concession reduces the stress caused by the radial resistance. Since the material in the string direction is a closed ring, the ring material itself is involved with each other after the string direction shrinks. The actual effect is no concession. As a result, the string stress is greatly expressed, and a tendency to crack is formed.
3.2 Contribution of cover ring valgus deformation rate to chord stress
After the radial part of the disc retracts, the annular cover ring is subjected to the moment of valgus. Let the contact point between the cover ring and the inner object be O, and the length ratio of the arm at both ends of O is α = lB / lA, as shown in FIG. 2. After shrinking, the natural position of the cover ring should be R- △ R outside the center of the circle, then the circumferential length of the cover ring is C1 = 2π (R- △ R). Owing to the obstruction of the lid contents, under the effect of the radial contraction force of the disc part, the lower bead B of the lid ring is turned outward around point O. In order to simplify the calculation, the rigid body model is adopted, and the horizontal distance of the bottom edge B of the cover ring from the fulcrum O of the contact between the inner object and the cover ring is △ r = α △ R = lB · △ R / lA. Since the natural position of the cover ring after contraction should be at R- △ R, the horizontal distance between the lower edge B and the upper edge A after hindered valgus:
The perimeter expansion rate PC1 of the lower edge B relative to the upper edge A is:
The relative shrinkage of the disc edge PC = △ C / C = △ R / R, it is clear that the relative perimeter elongation of the bottom edge B after eversion is the upper edge A and the disc edge (1 + α) (1 + △ R / R) times. among them. With the change of the position of the fulcrum O, in many cases α> 1, so the relative chord deformation of the lower edge of the cover ring B is much larger than the relative chord deformation at the edge of the disc. The shrinkage crack of the cover coincides with this Its inevitability.
4 Solutions and measures
In order to reduce the cracking tendency of the cover, according to the deformation of the lower edge of the cover ring. The length ratio of the arms on both sides of the point is related, which can reduce the position of the fulcrum O; improve the radial concession of the cover, and make the bottle mouth slightly inward to reduce the internal stress moment and internal stress. Adding a telescopic ring at the edge of the disc part of the cover in the radial direction can reduce the deformation of the disc edge, and eventually cause the displacement of the upper and lower edges of the ring part to decrease, thereby greatly reducing the internal resistance caused by the chord deformation of the ring. At present, some cover-shaped products are designed with a ring-shaped protruding structure according to the edge structure of the buckled object. It can reduce the radial resistance, but it cannot avoid the chord stress. Polymer materials have reduced flexibility at low temperatures, which directly affects the low-temperature stability of the lid-shaped structure and enhances brittleness.
The cold shrinkage crack of the cover meets the conditions of mechanical analysis starting from the lower edge of the cover ring. Under the assumption of the same warp and weft shrinkage, the radial and chord shrinkages are consistent, which has no significant effect on the directionality of the free shrinkage stress on the disk surface. The radial retreat of the cover reduces the generation of radial stress, but the chord directions are mutually involved and there is no room for retreat, which can produce larger stresses. The relative deformation rate of the ring caused by the tendency of the valgus of the lower edge of the cover ring increases the chord stress at the edge of the cover ring, which is the primary cause of cold shrinkage cracking. The radial directional crystallization of the injection molding process of polymer materials weakens the chord strength and is also a cause of cracking of the plastic cover. The use of targeted measures can reduce the tendency to crack.