1.2.4 Overview of melt rheology

A. Stress and strain during molding

The deformation and flow of polymers in various molding processes is result of external forces applied to them by molding equipment. Once polymer is loaded, an internal force will be generated internally that balances external force. The internal force per unit area is called stress. Depending on way force is applied, three types of stress are distinguished: shear stress τ, tensile stress and compressive stress δ. Changing shape and size of polymers under stress is called deformation. There are three strains used with three stress pairs: shear strain γ (reflecting shape change), tensile strain, and compressive strain ε (reflecting dimensional change). Formation During process, when an external force causing polymer melt to deform and flow, such as injection pressure of a screw or plunger, melt flow generally behaves like a laminar flow. At this time, flow resistance is mainly due to relationship between melt and gate system and inner wall of mold cavity, friction between them and viscosity between layers of melt flow, so injection pressure and flow resistance have a shear effect on polymer melt. During flow, polymer is mainly affected by shear stress and shear strain.

B. Viscoelasticity of flow deformation, hysteresis effect and relaxation

The essence of viscoelasticity: deformation of polymer is not instantaneous, there is a process, from continuous movement to movement of entire molecular chain, which is both viscous and elastic.

The hysteresis effect is that hysteretic effect of strain on stress becomes a hysteresis effect, and process of equilibrium between strain and stress becomes relaxation.

The hysteresis effect and polymer strain relaxation are common in molding process and often affect quality of product. For example, after a polymer is injected into a mold, if it can solidify under action of pressure maintenance and its slow cooling rate, polymer macromolecules can have enough time to deform and rearrange in cavity so that amount of deformation gradually reaches a balance with effects of injection pressure and holding pressure. After demoulding, there is no residual stress in product, which makes its size and shape stable. However, due to performance requirement in real production, above method is practically impossible to implement, so in real production, macromolecules can only be loosely stacked with each other according to shape of mold cavity, and there is no time for organization. they are close to each other, so amount of deformation is incompatible with injection pressure and holding pressure, after demoulding, there will be a large rest inside productcurrent stress, and macromolecules will continue to deform and rearrange over time to adapt to stress of casting. At same time, it helps loosely accumulated tissue structure to become denser. These phenomena are associated with relaxation. This is called strain aging or delayed strain of product in production. Aging often lasts for a long time, and sometimes it can even reach several months or years, so dimensions and shape of product change during operation and storage after demoulding. If appropriate decisions are not made, product quality requirements cannot be met.

For example, in injection molding, annealing injection molded products in high elastic state (Tg-Tf) temperature range can increase thermal motion of macromolecules, thereby shortening macromolecular deformation relaxation time, reducing size and shape of products. are quickly stabilized, and some plastic products can also be impregnated with high temperature water and some solvents (or water vapor, solvent vapor) for swelling annealing The swelling effect of solvent molecules during annealing is more effective than ordinary annealing. mechanical properties of plastic products, which is especially important for improving quality of PC, PPO, PS and other plastic products, such as PC, PPO and PS, which have relatively rigid chain segments and are prone to residual stresses during molding.

C, polymer rheology

The science that studies deformation and flow of matter is called rheology. Among them, polymer rheology mainly studies relationship between mechanical phenomena such as stress, strain, and strain rate of polymer materials under action of an external force and intrinsic viscosity, and various factors affecting these relationships. Such as polymer molecular structure, relative molecular weight size and distribution, temperature and pressure, etc.

(a) Newton's law of flow

Figure 1.4 Schematic diagram of Newton's law of flow

The flow of a liquid in a round pipe is divided into two forms: laminar flow and turbulent flow, which differ in Reynolds number Re of liquid. For a Newtonian fluid, since in laminar flow Re≤2100, and Reynolds number of polymer melt is usually much less than 2100 when polymeric materials are formed, their flow pattern can be considered as a laminar fluid flow. Laminar flow (Figure 1.4(a)) means that direction of flow of fluid particles is parallel to axis of flow channel, flow velocity is also same. The flow paths of all fluid particles are parallel to each other, but depends on friction of pipe wall, slippage between layers. The displacement speed is different, displacement speed around pipe wall is smallest, and displacement speed in center of pipe wall is largest. The greater viscosity, less likely shear deformation and flow, and lower viscosity, reverse is true. The viscosity of a small number of polymer melts is not sensitive to shear rate, which approximately corresponds to a Newtonian fluid, such as: PC, a copolymer of vinyl chloride and vinylidene chloride, polyamide and polyethylene terephthalate. Turbulent flow (Fig. 1.4(b)) is that fluid particles in tube not only flow in a direction parallel to axis, but also flow unevenly in transverse direction of pipe, and trajectory of particles is in a disordered state.

(b) Permissible fluid and apparent viscosity

The flow of polymers is much more complicated than that of low molecular weight liquids. With exception of a few such as PC, polyamide, vinyl chloride-vinylidene chloride copolymer and polyethylene terephthalate, most of them.

Due to complex long chain structure of macromolecules and interlocking with each other, flow law of high molecular weight polymers is much more complicated than that of low molecular weight liquids, which does not correspond to Newton's flow law. Stress and shear rate are no longer linear, and viscosity of liquid is no longer constant value (see Fig. 1.5 and 1.6). Typically, this type of fluid flow is called a non-Newtonian flow, and a fluid with this type of flow behavior is called a non-Newtonian fluid.

Figure 1.5. Flow curves for different types of liquids

In rheology of polymers, all non-Newtonian fluids subject to law of exponential flow are collectively referred to as viscous fluids. In a viscous liquid, when n<1 (usually about 0.25-0.67, flow index m=1/n is about 1.5-4, for example: PE, PVC, PMMA, PP, ABS, PS, HIPS, linear polyester, TPE, etc.) are called pseudoplastic fluids, and for n>1 they are expanding.

The more non-Newtonian fluid, smaller value of n and greater effect of shear rate on apparent viscosity.

(c) Rheological properties of pseudoplastic fluids and related issues

The rheological characteristics of a pseudoplastic fluid are as follows: in region of average shear rates, shear stress required for deformation and flow increases exponentially with a change in shear rate, and viscous resistance to deformation and flow is, i.e. apparent viscosity of fluid decreases exponentially with change in shear rate. This phenomenon is called “shear thinning” effect of pseudoplastic fluid (low shear rate γ≈102C-1, high shear rate γ≥106C-1).

The effect of thinning of polymer melt during shear is due to macromolecular structure of polymer and its deformability. When melt is subjected to pseudoplastic flow, if shear rate is increased, it will undoubtedly increase shear stress of macromolecular chain, so that disentanglement, elongation and slippage of macromolecular chain from its polymer network structure is intensified, displacement of chain segment (high elastic deformation) is relatively reduced, and van der Waals force (electrostatic attraction) between molecules will also gradually weaken, so free space in melt increases, viscosity decreases, and whole system tends to thin, thus presenting mechanical properties of reducing apparent viscosity at macroscopic level.

(d) Factors affecting rheological properties of polymers

(1) Effect of molecular structure on apparent viscosity

Generally speaking, macromolecular chains are flexible, flexible polymers are easily tangled, easily disentangled and oriented when flowing, and have strong non-Newtonian properties in melt flow, while macromolecular chains have high rigidity and intermolecular attraction. Polymers (such as polar polymers and crystalline polymers), melt temperature sensitivity increases and non-Newtonian ones decrease. Increasing temperature is useful for improving flow properties such as: PC, PS, PA, polyethylene terephthalate esters, etc., and when macromolecules contain larger pendant groups, free space in polymer will increase, which will increase pressure sensitivity of melt viscosity and temperature, such as PMMA and PS.

(2) Orelative molecular weight

When relative molecular weight of polymer is relatively large, macromolecular chain segment lengthens, movement of center of gravity of macromolecular chain slows down, and probability of relative displacement of chain segment is compensated. will increase, chain flexibility will increase, and entanglement will increase. Point increase, unwinding, elongation and slippage are difficult and generally require higher shear rate and longer shear action time, so melt viscosity and shear rate sensitivity viscosity (or non-Newtonian ) will also increase accordingly (see Fig. 1.7).

Figure 1.7 Influence of molecular weight on polymer flow curve

Figure 1.8 Effect of molecular weight distribution on polymer rheology

Polymers with a high relative molecular weight often have molding problems due to excessive viscosity. If these problems need to be solved, some low molecular weight substances (eg plasticizers, etc.) can be added to polymer to reduce relative molecular weight. and lower viscosity values. Help improve mobility.

(3) Relative molecular weight distribution

Table 1.3 Relationship between apparent viscosity and temperature of commonly used thermoplastics at constant shear rate

The difference in relative molecular weight between polymer macromolecules is called relative molecular weight distribution. The larger difference, wider distribution, and vice versa.

The influence of relative molecular weight distribution of polymers on melt viscosity is different for different shear forces and different shear rates. It decreases faster than viscosity at a narrow molecular weight (see Fig. 1.8). The effect of temperature on apparent viscosity is shown in Table 1.3.

(4) Influence of additives

After adding additives to polymer, force of interaction between macromolecules will change, and viscosity of melt will also change.

For example: addition of plasticizers and lubricants significantly reduces viscosity of melt, while most fillers increase viscosity.

(5) Effect of temperature on viscosity

Controlling processing temperature is an important means of controlling flow of polymers. As a rule, viscosity decreases with increasing temperature. Different polymers differ in their viscosity, temperature sensitivity. For same polymer in different temperature ranges, effect of temperature on the degree of secrecy is also different.

Figure 1.9 Relationship between apparent viscosity and melt temperature of several polymers

In case of a higher temperature, that is, at T>Tg+100℃, free volume in polymer melt is quite large, and flow viscosity mainly depends on structure of polymer chain itself, that is, movement ability of chain segment transition. At moment, relationship between polymer viscosity and temperature can be described by formula for η-T ratio of a low molecular weight liquid, that is, Arrhenius equation:

Among them is activation energy of viscous flow, A is a constant associated with structure, and R is gas constant.

For extrusion processing, especially twin screw extrusion processing, a combination of temperature and screw can be used to reduce melt processing viscosity and improve processing fluidity. In injection molding industry, process control method is mainly based on increasing temperature to reduce melt viscosity to improve flowability. It is mainly suitable for polymers whose viscosity is not very sensitive to shear rate or whose melt obeys Newton's flow law. The viscosity is very sensitive to temperature. Both injection molding machine and mold must have a high-precision temperature control system, otherwise any slight temperature change in barrel, nozzle or mold during molding process may cause a large change in viscosity of polymer melt, thereby affecting product Consistent casting quality.

(e) Effect of pressure on viscosity

When a polymer melt is injected, whether in preforming stage or injection stage, melt must withstand combined action of internal static pressure and external dynamic pressure. In pressure holding and feeding stage, polymer is usually subjected to a pressure of 150-200 MPa, and precision molding can reach 400 MPa. Under such a high pressure, free volume between molecular segments is compressed. Due to a decrease in free volume between molecular chains, approach of sections of macromolecular chain enhances intermolecular force, i.e., apparent viscosity increases.

When processing temperature is constant, compressibility of polymer melt is higher than that of a conventional liquid, and has a greater effect on viscosity. Because of different compressibility of polymers, pressure sensitivity of viscosity is also different, with greater sensitivity greater compressibility.

Polymers also increase viscosity due to increased pressure, which has same effect as lowering temperature of melt.

(f) Application of thermoplastic polymer rheology curve

(1) Determine reasonable process parameters according to rheological curve.

Any small change in shear rate will cause large fluctuations in viscosity, which will cause great difficulties in production control, i.e., unstable process conditions, unstable material flow, uneven density of end products, and adverse effects on injection molding. It is easy for product to cause a number of problems such as excessive residual stress and uneven shrinkage, but in latter region, flow characteristics cannot be effectively improved by changing shear rate, so reasonable process parameters can be selected to make melt The shear rate is maintained between front and rear regions.

(2) According to rheologistThe process of filling by low-temperature injection molding is adopted as an ic curve.

Currently, plastics processing companies recommend using low temperature mold filling technology. The low-temperature mold filling process needs to be realized by lowering melt temperature and increasing shear rate, which can not only shorten cooling time after product formation, improve productivity, but also reduce energy consumption in production.

D. Polymer melt flow in mold

(a) Final effect

When forming a polymer, polymer melt often needs to pass through flow channels with different cross-sectional dimensions. When melt passes through part where cross section of flow channel changes, elastic convergence or expansion occurs due to influence of interface. These movements are collectively referred to as terminal effect. Generally speaking, end effect is detrimental to quality of product. It can lead to problems such as product deformation and distortion, dimensional instability, excessive internal stress, and reduction in mechanical properties. Therefore, it must be overcome. The end effect is divided into entry effect and mold release .Two kinds of expansion.

(1) Entry Effect

Under pressure of flow, when polymer melt enters small boundary flow channel from flow channel with a large cross section, since cross section of flow channel changes from large to small, a converging flow will be generated at entrance to small channel. Flow cross-section channel (if transition part is not smooth, eddy currents will also be generated), this kind of converging flow will not only cause a large elastic deformation of melt, and thus consume a significant flow pressure, but also make melt flow in a small section of a certain length B turbulent flow occurs in flow channel. See figure 1.10 for a schematic diagram.

Figure 1.10 Input Effect Schematic Diagram

(2) Form Extension

When polymer melt flows out of trough or gate, volumetric expansion of melt flow is called mold expansion effect, which is actually an unstable flow caused by elastic recovery, also called Barus effect.

Factors affecting die expansion can also be divided into two types of factors: material factors and technological factors.

From point of view of material: The amount of elastic deformation of material affects degree of expansion of die and expansion position. Die swelling is aggravated by everything that causes an increase in elastic component of flow. In general, materials with high viscosity (high molecular weight), narrow molecular weight distribution, and strong non-Newtonian properties will retain more reversible elastic components in flow, and at same time, due to slow relaxation process, expansion phenomenon will be stronger when liquid flows out of nozzle significantly.

In terms of process factors, main influences are:

① Relationship between material melt temperature and die expansion. A corresponding increase in temperature of melt helps to reduce degree of expansion of matrix. Of course, an increase in temperature of melt will be limited by thermal stability of material and load of cooling device, and an increase in temperature of melt also increases energy consumption. If melt temperature is too low, it will impede flow of melt and increase mold swelling. Therefore, in actual production, if production can be carried out smoothly and quality products can be produced, according to this premise, temperature should be controlled as low as possible.

②Influence of stamp shape and size on stamp expansion. The degree of expansion of matrix increases with ratio of length to diameter of matrix, but this is not a linear relationship.

③Relationship between entry angle of convergence and degree of die expansion. Decreasing angle of convergence at input end can reduce die swelling. However, if angle of convergence of air intake is too small, length of nose will inevitably be increased. An appropriate input convergence angle must be selected.

④ Relationship between shear rate and die expansion ratio. The degree of matrix swelling increases with increasing shear rate.

(b) Unsteady flow and destruction of the melt

Table 1.4. Ultimate Shear Stress and Ultimate Shear Rate of Some Polymers

(1) Unstable stream

The chain of macromolecules will be fully straightened under extremely high shear rates (≥106 s-1), and if it continues to deform, it will show great elastic properties, as a result of which flow will not be able to maintain a stable laminar flow. , and melt enters a state of elastic disorder in which flow velocities at various points interfere with each other, a phenomenon commonly referred to as erratic flow of polymer melts. Table 1.4 shows ultimate shear stress and ultimate shear rate of some polymers.

(2) Melt failure

Figure 1.11. Extruded Shark Skin Distortion

After polymer melt passes through channel in mold in an unstable state, it will become uneven in thickness and dull, and surface will look rough like shark skin, as shown in Figure 1.11. In this case, if shear stress or shear rate continues to increase, melt will appear wavy, in form of a bamboo or a periodic spiral, and in more serious cases will break up into irregular fragments or small cylindrical blocks (Fig. 1.12). is called melt breaking.

Figure 2.12. Melt failure during high extrusion

Table 1.5 Values ​​of critical shear stress τCT and critical shear rate γCT of some plastic materials in unsteady flow

It can be considered that destruction of melt is total result of elastic deformation and elastic recovery of melt and is a general phenomenon. This general phenomenon is also related to nature of material, fluid flow channel geometry, and other factors. The values ​​of critical shear stress τCT and critical shear rate γCT of a number of plastic materials in unsteady flow are given in Table 1.5.

Measures to combat phenomenon of melt destruction:

①Adjust linear speed of melt in barrel;

②Increase temperature to increase ultimate stress and ultimate shear rate when melt causes flow instability;

③ When transitioning from a channel with a large cross section to a channel with a small cross section, reduce angle of convergence of channel with flow so that wall surface of transition is streamlined, which can increase shear rate limit during unstable flow.

(c) Mold filling flow

(1) Influence of gate and cavity geometry on mold filling flow

①The size of cross section of gate is very different from depth of cavity

When a small sprue faces directly into a deep mold cavity, when melt flows into cavity through sprue, it is easy to create an injection (or jet stream) phenomenon and mold will fill at high speed. Under influence of mold expansion, melt is very unstable in high-speed pouring, and cross-sectional size of gate is very different from depth of cavity. The surface is not only rough, but also prone to breakage. cavities, see Fig. 1.13(a). Due to occurrence of serpentine flow, molded parts will have grooved marks or surface defects due to folding.

②The difference between size of gate section and depth of cavity is small

The thickness of part is not too thick, melt will fill mold at an average speed, and after melt passes through gate, possibility of jet flow is reduced. If some process adjustments are made correctly (such as reducing injection speed, increasing injection temperature and mold temperature, etc.), a relatively smooth expansion (or expansion flow) will appear after melt enters the cavity, as shown in Fig. 1.13(b).

Figure 1.13. Performance at different melt filling rates

③Gating section size close to cavity depth

The thickness of part is very thin and melt usually doesn't splatter anymore. Under appropriate gate conditions, melt can expand and flow at a low rate to fill mold (Figure 1.13(c)). However, due to expansion effect of mouthpiece, melt will still have a period of unstable flow in cavity near gate.

In addition, in injection molding process, due to a change in certain process conditions or shape of cavity, melt filling mold at a low speed may suddenly change to a high speed, and filling flow will change original. Some expansion properties tend to become unsteady flow, similar to a serpentine stream (Fig. 1.13 (d)).

（2）Expand mobile filling point

The extended flow of polymer melt in mold cavity is a laminar flow. Figure 1.14 A plastic part is a thin-walled rectangular product of same thickness. The gate is installed at end, and width of gate is much smaller than width of product, and an experiment is carried out on filling process. Gradually increase injection volume to regularize resulting series of samples. It can be seen that leading edge motion characteristics follow the material flow.

The entire form filling process can be divided into three typical steps:

Figure 1.14 Melt front changes during mold filling

①At initial stage, when melt flows out of gate, it quickly forms an outflow source in mold cavity, starting from source, expanding and flowing to surface of surrounding cavity, showing material in form of a radial arc. head. As it develops, melt starting from outflow source will contact surface wall of mold around source, limited by mold, flow direction of each melt point will gradually turn towards front of mold, and expansion of flow enters second stage.

②Two features in intermediate transition stage: 1. Due to cooling and frictional effect of mold cavity wall surface on melt, forward flow speed at each melt point is different, and flow speed to middle is largest, so front head of material is still has shape of a round arc; other is that front head acts as a continuum in which points must interact with each other when flow velocity is different, i.e. low flow melt near cavity wall surface holds high flow melt in middle Cannot flow forward quickly but high-flow melt will in turn pull low-flow velocity, so forward flow velocity at each point will have a constant trend. With development of this stage, due to influence of air interface, temperature of front material head will drop, so a low-temperature viscoelastic melting film will form on front of material head, and at all points material head will be blocked by a melting film, forward flow rate will remain constant.

③The main stage of uniform movement of front feed head, its flow characteristics: due to blockage of low-temperature melt film, melt with a relatively high flow rate in middle of feed head is forced to rotate along arc surface of melt film, forming a kind of spouting flow, macromolecules in front feed head will create an orientation structure perpendicular to mold wall; at same time, due to cooling effect of low temperature mold wall temperature, mobility of orientation macromolecules near end of mold wall will be reduced, and mobility of other end will be reduced. Mainly retain original shape, so macromolecules will twist to a certain extent, and finally lead to vertical orientation of structure of front feed head, and at same time, corrugated surface will be formed in horizontal direction. But this corrugated surface can be smoothed out by melt pressure behind die. Therefore, molding of parts from thermoplastic polymers is a process in whichin which melt moves stagnantly under deceleration of the low-temperature melt film.

Figure 1.15. Flowchart of Advanced Flow Process

(3) Effect of flow on insert

The mold filling flow when melt encounters obstacles. For a cavity with a molding core or insert, flow of material is usually divided into two flows along direction of flow, when melt fills mold, bypassing obstacles, and then converges at At, in this case, welding lines are often formed at melt confluence, where strength of product decreases and appearance deteriorates. .

In mold cavity, polymer melt flows around obstacles of various cross-sectional shapes, as shown in fig. 1.16.

①Velocity change: best cross-sectional shape of obstacle is cylindrical, since speed of melt particle passing around cylindrical obstacle gradually increases and decreases, and fluctuation range is smallest.

②Convergence situation: two melt streams bypass obstacle and converge at a certain distance from obstacle, forming a closed triangular area without melt behind obstacle. Rectangular obstacle is most obvious, and cylindrical is most obvious. Weak and almost imperceptible with a diamond shape. There is no melt in triangular region because there is air in it, which not only affects merging of two melt streams, but also causes coking and blackening of surrounding plastic when air is highly compressed by melt stream and rapidly exothermic.

Figure 1.16. Change in speed υ of thermoplastic melt flow around curly obstacles

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