Pharma glass properties - Part 10. Strength vs. toughness

Hello everyone – the terms “strength” and “toughness” are often used interchangeably, but they are actually very different concepts within the context of mechanical properties of materials. Part 6 in this series provided a high-level overview on the strength of pharmaceutical glass packaging.? One key takeaway from that article is that the practical strength of glass is generally much, much lower than the theoretical maximum strength due to flaws that act as concentrators of applied tensile stress.?? Strength is therefore more of a pseudo-property for brittle solids such as glass that are highly sensitive to the presence of these flaws.? In contrast, the toughness of glass is an actual material property that is relatively constant for compositions that are considered generally suitable for parenteral packaging.

My prior post also glossed over the reality that there are multiple types of strength that can be considered, including but not limited to yield strength, tensile strength, and compressive strength.? Yield strength refers to the maximum stress that a material can withstand before it begins to undergo plastic deformation – i.e., an irreversible change in shape in response to an applied stress.? This is in contrast to elastic deformation, in which an object returns to its original shape after the removal of an applied stress.? A common metal paperclip provides an easy demonstration of these ideas – you intuitively know how the shape of a paperclip can be permanently altered if a sufficiently large stress is applied.? However, the concept of yield strength is not fully applicable to brittle solids such as glass (see Footnote 1).? The important point here is that brittle solids are expected to perform differently under tensile (pulling apart) and compressive (pushing together) loading conditions.? Tensile strength will generally be lower than compressive strength because of flaws that concentrate the applied stress, as illustrated n Figure 1.? With all of that said, let’s attempt to generalize what is meant by “strength”.? I’m going to define it as a measure of a material’s ability to withstand stress leading to some type of permanent deformation.

So how is toughness different from strength?? A graphical example is a helpful starting point.? Figure 2 shows a stress-strain curve for hypothetical brittle and ductile materials – e.g., a glass and a metal, respectively.? The stress axis is reporting the amount of stress being applied to the material (see Footnote 2); strain is the amount of deformation exhibited in response to the applied stress.? In this case, we see that the brittle material is able to support a stress that exceeds the ductile material, but then it immediately fails at a relatively low amount of strain.? In contrast, the ductile material is able to undergo a significant amount of deformation, although we would also conclude that it is weaker than the brittle solid based on the maximum stress before failure (see Footnote 3).? The total area under the curves (the shaded regions) are one way to think about toughness – more area translates to more energy needed to propagate a complete fracture of a material.? And so in this case, we would say the ductile material is tougher than the brittle material.? It’s common at this point in similar discussions to say that strength and toughness tend to be inversely correlated – i.e., very strong materials tend to be low toughness and vice versa).? This statement can be true, but I think it’s worth making at least two points of clarification.

Clarifying point #1 – I used Figure 2 to present the idea of toughness in a general way, but this is not necessarily a true measure of the fundamental material property that I would call “fracture toughness”.? For example, we already know that the practical tensile strength of glass is controlled by the presence of flaws that amplify applied loads.? Figure 2 tells us nothing about these flaws, which in turn can lead to erroneous conclusions about material performance and catastrophic consequences for product design.? A more informed approach relies on fracture mechanics, a discipline that explicitly considers the impact of defects on mechanical reliability.? A complete treatment of fracture mechanics is way beyond the scope of this post.? Simply put, fracture mechanics can be used to predict the “stress intensity factor” caused by a hypothetical flaw of known geometry under a given set of loading conditions.? Increasing the load and/or the length of the flaw is expected to increase this stress intensity factor (see Footnote 4), which in turn can eventually cross a threshold at which the flaw will stably propagate within the material.? This critical stress intensity factor, otherwise known as fracture toughness, is a true material property that can be measured by various methods using samples containing intentional defects (see Footnote 5).? The units of fracture toughness seem a bit non-intuitive at first glance (MPa-m^0.5 in SI units) – you can think of this in terms of stress multiplied by the square root of flaw length.? The fracture toughness of inorganic oxide glasses of the sort used for parenteral packaging have a fairly constant fracture toughness of approximately 0.7 MPa-m^0.5…which leads to my next point.

Clarifying point #2 – the strength and fracture toughness values that are practically attainable by inorganic oxide glasses fall within a relatively narrow portion of the materials spectrum.? Figure 3 is an example of what is sometimes called an “Ashby plot” that is used to visualize regions of material performance.? Two properties are plotted against each other in a manner that can be very useful in considering the tradeoffs that inevitably occur during product design.? The blue-colored regions describing the properties of various classes of materials (polymers, glasses, ceramics, metals, etc.) are all based on measurements performed under tensile loading conditions.? As a result, we see an apparent conflict with a general statement that I made earlier in this post – i.e., there tends to be an indirect relationship between strength and toughness.? The blue portion of this plot would suggest the exact opposite, a direct relationship.? However, the original version of this plot doesn’t necessarily account for typical materials-specific use cases.? Instead, I have overlaid another yellow-colored region that approximates the performance of glass under compressive loading – roughly 10 times greater than the tensile strength region.? Based on this alternate view, we can begin to see how some (but certainly not all) ductile materials can exhibit a lower strength but higher fracture toughness.

Circling back then to the start of this post – I hope to have provided you with some basic information that explains why strength and toughness are not interchangeable terms.? To state things simply -- the type of inorganic oxide glasses used as a material of construction for parenteral packaging isn’t particularly tough, but it can be reasonably strong.

Questions or comments? – please leave them below or feel free to directly contact me.

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Footnotes

1.?????? I am also going to ignore for now the differences in behavior that are observed with glass at relatively small scales.? For example, glass composition can have a significant influence on how the material responds to indentation from a point load.? The highly localized stress caused by indentation can cause plastic deformation to occur in the form of compaction and/or viscous flow.

2.?????? I need to clarify that the tests performed to evaluate things like tensile and compressive strength are not actually measuring stress directly.? The testing machines are instead programmed to apply a particular force to a sample.? The stress can then be calculated as the applied load divided by the cross-sectional area for simple sample geometries under uniaxial loading conditions.? Slightly more complicated loading conditions can still be translated to relatively basic formulas for calculating stress provided that the sample geometry is simple.? A stress at failure can still be estimated when testing a more geometrically complex object like a parenteral glass container, but it requires more work.? Techniques such as finite element analysis (FEA) can be used to construct a model that predicts the stresses that develop within an object of interest under a defined load.? For example, a FEA model could be used to predict the maximum tensile stress that is generated in a 10R vial under a vertical load that might be used as a proxy for the capping process.? Just remember that knowing the maximum tensile stress is helpful but not the whole story. ?Brittle solids such as glass fail when a sufficiently large tensile stress interacts with a sufficiently large flaw.? A glass container can therefore break in response to a stress that is lower than the overall maximum if it happens to be in a region of the container in which there is a relatively large flaw. ?As a result, we often simply report the results of mechanical testing of geometrically complex objects as the load (not stress) at failure.

3.?????? Readers who are familiar with this topic will recognize that I have drawn a simplified version of what a real stress-strain curve might look like for a ductile metal – no references to yield point, strain hardening, etc.? The real focus of this article is brittle solids, and so please forgive my shortcuts.

4.?????? Various real-world phenomena can lead to deviations from this basic framework.? For example, there is so-called “R-curve behavior” in which (most commonly) the resistance to flaw propagation can actually increase with increasing flaw length.? This may occur when surface friction or microstructural features (e.g., individual grains within a polycrystalline ceramic) interact within the “wake” of the advancing flaw to shield the flaw tip from experiencing the maximum applied load.? On a related note, this an area where the term “crack” is often interchangeably used for flaw.? As I’ve mentioned in prior posts, I intentionally try to reserve the word “crack” for the situation that is more relevant to pharmaceutical packaging – i.e., a continuous path that spans the wall of container.? Despite my best attempts, I found myself repeatedly writing crack when I meant to say flaw throughout this post – old habits die hard.

5.?????? There is another approach to estimating fracture toughness based on pressing a diamond indenter into a nominally pristine material surface.? Dimensional measurements of the resulting indentation and associated flaws are used as inputs for models that generally consider other material properties such as hardness, elastic modulus, etc. to calculate fracture toughness.? The use of indentation methods is attractive because sample preparation and experimental execution are much easier than other methods.? However, the applicability of these methods as a true measure of fracture toughness has been called into question – cf. Quinn and Bradt (2007), Journal of the American Ceramic Society, 90: 673-680.